"We thought: 'Let's have a stage the shape of Texas.'" In dark glasses, 10-gallon hat, cowboy boots and – of course – long beard, ZZ Top's bassist Dusty Hill is remembering the time the band decided to take their home state to the world – or as much of it as they could reach. "There was a screen in the back that looked like the desert. Then, let's get some animals. We had a longhorn buffalo that came up on hydraulic lifts before and at the closing of the show – you don't want it up there during the show. Bad idea. Javelina [skunk pigs], which are mean little guys. And a coupla rattlesnakes in a Plexiglass dome. You could put your foot on top of that glass."

This was 1976, and the Worldwide Texas Tour, one of the greatest follies in rock history. "There were six or eight semi-tractor trailers to carry the gear and they were painted in a desert scene, and they were done in order," Hill continues. "They had to travel down the highway in a certain order so the scene went from one to another."

When Hill says the tour "cost us", he's not exaggerating. The cost of caring for the animals alone was reportedly $140,000 (£88,000). And then there was the further problem of trying to play for audiences outside the US. "We were trying to take it to Europe," Hill says, "but the quarantine laws hooked us."

He reflects for a moment, inscrutable behind his shades, before observing, gently: "If we ever have a problem, it's not comin' up with ideas. It's stoppin' us."

There may well be plenty of people for whom the notion that ZZ Top are a band of ideas is as ridiculous as calling Skrillex one of our more sensitive singer-songwriters. Are the Texan trio not just the American answer to Status Quo? The band with two members with beards and – get this – one without, but it doesn't matter because his name is Beard?

Well, maybe. But there's a whole lot more to ZZ Top. Actually, how's about this for a notion: ZZ Top are in fact an absurdist modern art project whose chosen medium is the 12-bar blues. "I like that," says Billy F Gibbons, singer, guitarist, and other beard (gingerish, rather than greying like Hill's). "Jim Dickinson, our favourite crazed record producer out of the Memphis area, called me aside and he said: 'Yeah, ZZ Top. You're like the Dalí of the Delta.' I'll take that. A high compliment in my esteem."

The absurdism is there in ZZ Top's obsession with the ephemera of US pop culture: the Cheap Sunglasses and TV Dinners of their songs. It's there in the matching stage uniforms. It's there in the music, too, in the way they started assimilating new-wave influences from 1979's Degüello album, in the way their comeback single earlier this year was a cover of a Houston hip-hop song. It's there in their surrealist approach to the world (when Gibbons was once asked why their 1983 smash-hit album Eliminator was their first record without a Spanish title, he explained it was in fact called El Iminator).

Most of all, the absurdism is there in Gibbons – whose every word appears to be the setup to an elaborate practical joke that he may or may not choose to follow through with. Even his dressing-room table backstage at Merriweather Post Pavilion in suburban Maryland – where ZZ Top are playing a festival date at the personal request of headliner Jack White – has its concession to oddness: a personalised memo pad headed: "BFG. Friend of Eric Clapton."

"It was kind of a prank," Gibbons says. "I went in to get a business card printed up at the local Kinko's. And when I came to collect it they showed me the sample, and said: 'Shall we run with it? Do you approve?' I said: 'I'll take it.' OK. That's Joke No 1."

Joke No 2 begins with Gibbons being asked to record a part for a solo record by Sam Moore, and leaving his card on the mixing desk in case he was required to return – not knowing Clapton was due in the studio the next day. "Fast-forward to Eric's seven nights at the Royal Albert Hall. His minder tracked me down and said: 'Eric would like to see you.' I saw the show. On the exit, he said: 'We're going to see Eric.' Fine. Go down to the bowels of the Royal Albert Hall, there was a small door, and one small sofa, and Eric was sitting there. He said: 'I have two requests. I understand the Gibson guitar company is making a tribute to your famous Sunburst. Can you get me in the queue to get one?' 'I'm pretty sure. And what's the second request?' 'Can I have one of your business cards?' Busted!" He laughs delightedly.

Gibbons is steeped in the blues – brought to him by Big Stella, the housekeeper at his childhood home in Houston – but also in art. When ZZ Top were on hiatus in the late 1970s, before Degüello, he went to Paris to pursue it. "I had some buddies from Houston that had started this consortium of new-day surrealism – more than just a tip of the hat to the Dada guys. We were doing Xerox art and it was not so great, but the effect … If you took an image and then printed it out and then re-imaged that, the more generations you did the degradations started to set in. It was real vivid. From a technical standpoint it was just degradation, but from an artistic standpoint it was an enrichment of a visual experience."

He set himself the challenge of bringing that same combination of degradation and enrichment to the blues. Then punk came along and offered him the means to do so, though not without help from Sir Freddie Laker. In September 1977, Laker launched his Skytrain – a budget-priced flight between New York and Gatwick. When Gibbons saw the flights were launching for $99, he resolved to take his English father and Irish mother to the British Isles. "So we go and we drop down when this punk explosion was happening," he says. "One thing I can assure you: I remain open to the effects of the energy events. That really got my attention. The anger and the angst did not allow anything more than: 'I don't have time to practise too long, I'm just gonna give it to ya like I got it.'"

Returning to the South, he realised he wasn't the only one who had noticed. Over in Georgia, the B-52s were presenting a kitschy, Dayglo version of American pop culture inspired by punk, and he decided to respond. "They had the song Rock Lobster, and Party on the Patio was: "You think you can get punky? We're gonna get punky!" In truth, the music ZZ Top started making at this time was not awfully punky – though it could be tinny, occasionally tuneless and very, very odd – but it locates precisely the point at which ZZ Top's songs embraced subjects besides beer drinkin', hell raisin', brothels and bad women – that's how punk liberated them.

The obsession with the detritus of American life, Gibbons says, gave the band their real voice: finally, they weren't imitators or copyists. As he puts it, finding their own subject matter enabled them to be blues musicians without the carping about them being white and never having picked cotton. "I knew it was OK because there was no way ZZ Top would lose their blues."

The blues came early into the lives of both Hill and Gibbons, in Dallas and Houston respectively. "My mother listened to blues records when I was a small child," Hill remembers. "Back then, without sounding so ancient, kids would go to each others' houses, bring some records to play. And I'd bring Muddy Waters or Son House or something, and the parents of these other kids would almost freak out: 'What the fuck are you bringing here?' Whoa! I thought everybody had these records, because that's what I had."

"A few nights a week we'd get to go down to stay with Big Stella in her house," Gibbons says. "She had four kids – there was, ironically, Little Stella, Dorothy, Minnie and Johnny, and then my younger sister Pam and I. And Big Stella would often be tuckered out and gone to sleep by 8.30, 9 o'clock. Little Stella would grab my sister and I and walk us down to the corner where there was a little juke joint. I say a little juke joint – it was owned by Don Robey. Don Robey was the black entrepreneur that had Duke Records, Peacock Records, he owned the Bronze Peacock, the El Dorado Ballroom, the Buffalo Booking Agency. Suffice it to say that that was the start, because it spawned the interest. And I had the immediacy. When I was six years old I saw Jimmy Reed, Howlin' Wolf, some of the giants."

The turning point for Gibbons, though, was seeing Elvis in his glorious, Brylcreemed pomp. "My mom took my younger sister and I to see Elvis in Houston in 1956. It was one of these big showcase shows. Brenda Lee was on the bill. Elvis by this time had topped up. Texas was a big starting point for Elvis and fortunately my mom was a fan and we got to go see it. And I was like: 'That's it.'"

Both Gibbons and Hill started playing music young, too. Gibbons was a member of a psychedelic band called the Moving Sidewalks, whose song 99th Floor is one of the enduring classics of the garage punk boom. Hill and Beard joined the American Blues, whose gimmick was dyeing their hair blue. But in a state as conservative as Texas, being part of the underground wasn't a passport to acceptance. "Being a musician in Texas had its own set of risks ," says Hill, perhaps remembering their contemporary Roky Erickson of the 13th Floor Elevators, who ended up institutionalised. "In the 60s in Texas. I got probably less shit about having blue hair than about having long hair, because I believe they thought I was crazy."

Gibbons is an odd thinker, darting off on tangents in his easy drawl, speaking softly and so slowly that his words appear weighted with import. It's only when reading them back that one realises quite how bonkers some of what he says sounds. For instance, a question about whether hip-hop is the modern blues sees him asserting the world will undergo a fundamental change in 2024. "There will be scientifically acknowledgeable events comparable to the appearance of language or the appearance of life," he says. "We're already starting to see it: chemical control of ageing, artificial eyesight for the blind. We're racing toward this moment when all that is knowable becomes known. The delivery mechanism? What will it be? A blinding flash of lightning? Or does everyone drink a sip of water at the same time? Does everybody hit the return key? But I'm getting a little esoteric here. Back to the blues, please."

I have no idea if he believe this. He conveys it with absolute solemnity, but maybe he's having me on, testing my credulity. A couple of times he brings up emails on his Macbook to show me pictures – a photo Jeff Beck has sent over of a vintage car he has rebuilt; the Rolling Stones' 1972 lightshow, an inspiration to the current Top stage set – and asks that I pause my recorder, as if it might somehow be able to absorb the contents of his computer by digital osmosis. But he's diligent, too – after an hour he asks to stop the interview, and whisks me to the side of the stage to watch the end of Jack White's set. It's an "is this really happening?" moment, watching White play Seven Nation Army from a few feet away, standing alongside this totem of American rock, yet it leads me to fear the interview will not resume. But no, once White has finished we stalk back to the tour bus and carry on, as if the interruption had never happened.

Gibbons's unexpected way of viewing the world, though, has paid dividends. Take Eliminator, the album that made ZZ Top the most unlikely superstars in the MTV firmament back in the 80s. It sounds like a band making a calculated attempt to crack the mainstream, with its smooth, shiny finish, its beats processed to metronomic perfection, its hooks sharpened and placed front and centre. In part, it was the result of Gibbons's exposure to UK synth bands such as Orchestral Manouevres in the Dark and Depeche Mode. And in part it was a product of Gibbons's personal quest to discover perfect time.

"Midi was invented and all these instruments were talking to each other, and you could make this one the slave to this one. The crack in the code was the fact that the drum machine introduced for the first time to the listening ear close-to-perfect time, which had been the aspiration of musicians since the invention of the metronome," he says.

"So we didn't abandon the blues backdrop. We kept a rock focus. But all of a sudden we're paying attention to good timing, good tuning. Simple.

Earlier this year, ZZ Top released their first album for nine years. La Futura is the rarest of things from a veteran band – a record that stands among the best they've done. Its guitars roar and growl, Gibbons's voice a toxic gargle in counter to Hill's higher, truer yell. And it begins with the year's most unlikely cover version: I Gotsta Get Paid, a version of DJ DMD's crack-dealing hip-hop anthem 25 Lighters. As with so many things in ZZ Top's career, it owes as much to chance as to design.

They were short one song as the sessions for La Futura came to an end. Gibbons cast his mind back to 1996, when the band's studio was being refurbished and instead they were recording in a place used by the local hip-hop crews. "There was three rooms – Studio A on the left, Studio B on the far right, connected by the collective chillout lounge. And that's where it all started to break the ice. The hip-hop guys wanted to know: 'Hey, how do you do this guitar stuff?' But we wanted to know: 'Well, how do you program this drum? We like the backbeats!' I became transfixed on that one track 25 Lighters. Fast-forward to the last promised track deliverable to round out La Futura. I'm sittin' there talkin' about the good ol' days with the engineers, G Moon and Joe Hardy, and I said: 'You remember that 25 Lighters? Man, that thing has been driving me nuts.' Well, Mr Moon was watching some Lightnin' Hopkins videos on YouTube and as luck would have it, the two energies came together. Simple, to the point. No, we're not going to be a rap or hip-hop group by any stretch of the imagination. What we do is, we're gonna make it ZZ Top. Bluesy, yeah. But it's all Houston ghetto."

Next week, ZZ Top's 43-year stint as one of the world's most recognisable rock'n'roll bands will be honoured in London, when they pick up the Living Legends gong at the Classic Rock Magazine awards. Watching them on stage in Maryland, you see the affection in which they are held by very different groups of people of very different ages. The men the same age as them whoop for early blues like Waitin' for the Bus/Jesus Just Left Chicago; there are twentysomethings punching the air to the big hits from Eliminator – Gimme All Your Lovin', Legs and Sharp Dressed Man. There are hipsters getting down to I Gotsta Get Paid. They are loved. There's even a cheer when drummer Frank Beard's dog Gizzmo runs onstage at the end of the set (he has his own set-up in the dressing room, complete with skull-and-crossbones water bowl) and scampers about the amps.

"If there are people who admire us and what we do, that's a huge compliment," Hill says. "As long as it doesn't get too crazy. People are all the time telling me stories: they named their son after me, or more than likely their dog. Or they got a tattoo. Or had their first sexual encounter when a song of ours was playing. Thank you for the compliment, I really wish I had been there."