The singer's much-anticipated series of concerts are a sell-out, her return to the stage heralded by critics everywhere. Yet her particular brand of carefully crafted fantasy was not always so widely acclaimed

In 2014, the idea of Kate Bush as a pop star seems almost unbelievable. Did it actually happen, that run of singles so strange and yet so strong that they rose to the higher reaches of the hit parade, rubbing shoulders with Showaddywaddy and the Nolans on Top of the Pops? How did such an unearthly voice and unleashed imagination ever infiltrate the mundane mainstream, get playlisted on daytime Radio 1, profiled on Nationwide, parodied on Not the Nine O'Clock News?

The string of hits from Wuthering Heights to Cloudbusting is almost unrivalled for sustained brilliance and escalating oddness – only the Beatles, from start to finish, and Bowie, from Space Oddity to Fashion, surpass it.

Just take a look at the high points, year by year …

1978: Wuthering Heights. Gothic romance distilled into four-and-a-half minutes of gaseous rhapsody, this was released as her first single at Bush's insistence in the face of opposition from seasoned and cautious EMI executives; wilfulness vindicated by the month it spent at the top of the charts.

1979: Them Heavy People (the radio cut from the On Stage EP), which namedropped the Russian mystic Gurdjieff and Sufi whirling dervishes, a celebration of being intellectually-emotionally expanded: "it's nearly killing me … what a lovely feeling".

1980: Breathing, a chillingly claustrophobic sound-picture of slow death through radiation sickness after the bomb drops: "Chips of plutonium/are twinkling in every lung." Swiftly followed by Army Dreamers: perhaps the best, certainly the most subtle of anti-war songs, inventing and rendering obsolete Let England Shake a couple of decades ahead of schedule.

1981: Sat in Your Lap. Avant-pop stampede of pounding percussion and deranged shrieks, a sister-song to Public Image Ltd's Flowers of Romance, but lyrically about the quest for knowledge: "I want to be a scholar!"

1982: The Dreaming, Bush's first real flop, but artistically a triumph: inspired by Australian indigenous culture and music, it's a Fairlight fairytale that used smashed-marble for percussion sounds and prophesised a completely alternate future for sampling-based pop than what would actually transpire.

1985: Running Up That Hill, an ecstastic protest against the limits of identity and empathy, pre-empting Prince's similarly inspired If I Was Your Girlfriend by a couple of years. Then Cloudbusting, a song/video about psychologist-turned-mystic Wilhelm Reich's attempts to build a rain-making machine, as seen through the faithful eyes of small son Peter.

As words and as music, none of these scream "hit single". Yet all but one of them were. It's therefore hardly surprising that Bush's name gets reeled out, with varying degrees of appropriateness, as the ancestor for any new female artist trying to merge glamour, conceptualism, innovation and autonomy: recent examples include Grimes, Julia Holter and FKA Twigs. Yet, strange as it seems now, Bush was not always impregnably cool. In fact, despite her massive record sales and mainstream fame, she was not afforded much respect by critics or hip listeners in the late 1970s.

This was partly a matter of timing. After a year of being developed by EMI, (who funded her while she "grew up", expanding her horizons and honing her craft) Bush emerged into a British music scene transformed by punk. Both her sound and her look seemed conventionally feminine when juxtaposed with ferociously confrontational performers such as Siouxsie Sioux and Poly Styrene, who shredded expectations of how the female voice should sound and who shattered taboos with their lyrical content and appearance. Bush's fantastical lyrics, influenced by children's literature, esoteric mystical knowledge, daydreams and the lore and legends of old Albion, seemed irrelevant, and deficient in street-cred at a time of tower-block social realism and agit-prop. Her odd combo of artiness and artlessness, and the way she came across in interviews – at once guileless and guarded – made her a target for music-press mockery. Her music was often dismissed as a middlebrow soft option, easy listening with literary affectations.

Despite being as young or younger than, say, the Slits, Bush seemed Old Wave: she belonged with the generation of musicians who had emerged during the 1960s ("boring old farts", as the punk press called them). Some of these BOFs were indeed her mentors, friends, and collaborators: David Gilmour, Peter Gabriel and Roy Harper. Growing up, her sensibility was shaped by her older brothers, in particular the musical tastes and spiritual interests of Jay, 13 years her senior and a true 60s cat.

Punk often sneered at "art" as airy-fairy, bourgeois self-indulgence, but its ranks were full of art-school graduates and this artiness blossomed with the sound, design and stage presentation of bands such as Wire and Talking Heads. Yet Bush's music seemed the wrong kind of "arty": ornate rather than angular, overly decorative and decorous. It was the sort of musically accomplished, well-arranged, album-oriented art-pop that EMI had been comfortable with since the Beatles and had pursued with Pink Floyd, Cockney Rebel and Queen. They signed Bush expressly as the first major British female exponent of this genteel genre.

And that's where Bush was situated on her first two albums, The Kick Inside and Lionheart: somewhere at the crossroads of singer-songwriter pop, the lighter side of prog, and the highbrow end of glam. Like Bowie, she studied mime with Lindsay Kemp, took classes in dance, and made a series of striking, inventive videos. EMI's Bob Mercer hailed Bush as "a completely audio-visual artist" and spoke of the company's intention to break her in America through television rather than radio (this, several years before MTV even existed). Her one and only tour was a theatrical mega-production in the rigidly choreographed tradition of Diamond Dogs, all dancers and costume changes and no-expense-spared staging. Reviewing one of the 1979 concerts for NME, Charles Shaar Murray typified the general rock press attitude towards Bush at that point, scornfully describing the show as a throw-back to "all the unpleasant aspects of David Bowie in the Mainman era.... [Bowie manager/Mainman boss] Tony DeFries would've loved you seven years ago, Kate, and seven years ago maybe I would've too. But these days I'm past the stage of admiring people desperate to dazzle and bemuse, and I wish you were past the stage of trying those tricks yourself." Spectacle, in the immediate years after punk, was considered a narcissistic star trip, fundamentally non-egalitarian.

Abandoning the live arena altogether, Bush plunged deeper into the studio, exploring its capacities for illusion-spinning: a theatricality of the mind's eye, conjured through sound. Her music got more challenging, harder to ignore or deny, as she gradually assumed total control. On 1980's Never For Ever, Bush co-produces but is clearly calling the shots: the result is like the missing link between Laura Ashley and Laurie Anderson. Two years later, the production and arrangement entirely in Bush's hands, came her wholly unfettered mistress-piece: The Dreaming.

Bush revelled in the empowerment, declaring that "the freedom you feel when you're actually in control of your own music is fantastic" but giving the emotion a distinctly female inflection: "as soon as you get your hands on the production, it becomes your baby. That's really exciting for me, because you do everything for your own child."

Integral to her seizing of the means of musical production was Bush's ardent embrace of the Fairlight sampler, at that time an expensive plaything reserved for an elite of art-rock superstars such as herself and Peter Gabriel. Years ahead of The Art of Noise or Mantronix, she became a sampling pioneer, at a time when very few women outside the realm of academic electronic composers were involved with cutting-edge music-making technology.

Armed with the Fairlight and other state-of-the-art machines, Bush pushed her existing maximalist tendencies to the brink of overload, making The Dreaming a delirious, head-spinning experience. Paradoxically, such a sound was born not through spontaneity and randomness, but obsessive-compulsive meticulousness. It took a control freak to create such a freak-out.

Particularly arresting were the new uses Bush was making of her voice: tracks such as Pull Out the Pin and Suspended in Gaffa teemed with a panoply of exaggerated accents and jarring phrasings, as Bush applied thespian emphasis on particular words or syllables, and developed a whole new vocabulary of harsh shrieks and throat-scorched yelps. Emotions clashed or merged into hybrids impossible to parse. And all this was before she let rip with the studio effects and stereophonic trickery, as on Leave it Open, with its birds-on-helium twitters. Pretentious in the best sense of the word, Bush in the early 80s became one of those artists, such as the Associates or Japan, who caused Radio 1 daytime DJs to titter nervously, or be openly derisive.

As the postpunk era gave way to the glossy, overproduced 80s, suddenly Bush's sumptuous soundscapes made more sense than they had during the era of 2 Tone and Joy Division. Hounds of Love was both a commercial and critical smash. For the first time, really, Bush was hip, raved about by music journalists without any hint of apologia or reservation. With bands such as the Banshees and the Bunnymen opting for lavish orchestrations, Bush now seemed less like a throwback to pre-punk times and more like a sort of posh auntie to the goths. Indeed, she came from the very same southern-edge-of-London suburbia as Siouxsie.

Of the ethereal-girl artists emerging in the mid-80s, Elizabeth Fraser was the most clearly indebted – indeed, the frou-frou side of Cocteau Twins could be traced to a single song on Never For Ever, Delius (Song of Summer). Björk's starburst of vocal euphoria likewise owed much to Bush. Enya, formerly of Clannad, followed in Bush's footsteps in her explorations of synths and sampling, as well as taking vocal multi-tracking to the dizzy limit.

The 90s saw the arrival of Tori Amos, whose piano-driven confessionals blatantly drew on Bush's ornate early sound. But there were less obvious inheritors, too. Touring their first album, Suede liked to air Wuthering Heights immediately before going onstage: Brett Anderson placed Bush in his personal trinity of utterly English ancestors, alongside Bowie and Morrissey. Esoteric-industrial duo Coil hailed Bush as "a very powerful witch", possibly knowing about – or simply sensing – the Bush family's shared enchantment with the ideas of Gurdjieff who, among other things, explored the magical effects of particular musical chords. Closeted fans started to emerge from the unlikeliest places: Johnny Rotten, for instance, gushed about the "beauty beyond belief" of Bush's music.

But even as her deity status in the alternative-music pantheon gained lustre, Bush's creative ouput dimmed: album releases became sporadic, the gaps between grew longer and the impression made on public consciousness with each record fainter. Just about everybody knows Wuthering and Running Up That Hill, but how many common-or-garden pop punters could sing, or even name, a single off The Sensual World or The Red Shoes? In the 2000s, Aerial and 50 Words For Snow, quiet records both, received admiring notices, the kind of "glad you're back" reviews that Iconic Artists receive as a reward for a lifetime of achievement and the cumulative gratitude and affection inspired thereby.

Meanwhile, as a kind of public figure, Bush virtually disappeared.

It is striking how little we know about Kate Bush, how completely she's preserved her privacy.

During the critical phase of their rise to fame and often for a long time after it was strictly necessary, figures such as Bowie, Eno or Morrissey made an art form out of the music paper interview, using it as a forum to expound ideas, to hone or extend the public persona, to engage in mischief or mystique. But Bush never shone in that context. Interviews are a chore, a distraction from her real work, a waste of her time. Faced by a journalist's microphone, Bush is reserved, dry, ungenerous – the exact opposite of how she is faced by a microphone in a recording studio.

I interviewed Bush around the time of The Red Shoes and found it a frustrating experience. It's not that she was terse or tetchy; she answered every question, mostly at decent-enough length, and got evasive only once or twice. But there was a glazed quality to the conversation, in the sense of trance-like and mechanical, but also "glazed" like a ceramic film forming an invisible barrier. There was a sense of non-encounter. I would attribute it to my own failings as an interviewer, except that my wife, far more adept at getting people to open up, had the same experience a month later. Fred Vermorel, the author of not one but two brilliantly unorthodox biographies of Bush, has written about the way "she will neutralise you by dissolving her presence in a polite fog". And if you look through the archive of her interviews, it's clear she's been doing that for years: it is striking how little of the vividness and exuberance of her music is allowed into the interviews.

In a 1993 TV doc, Bush spoke bluntly and almost disdainfully of her discomfort with interviews, her feeling that everything she has to say is in the work and that there it is said more eloquently than she could ever be in speech – a view that is echoed by her plea to fans to refrain from taking photographs and videos during her forthcoming concerts. But the real issue, I suspect, is that to consent to an interview is to allow oneself to be framed and interpreted, to have your utterances snipped up and shunted around the page. The obvious analogy would be a singer-songwriter who laid down the vocal melody but handed over the arrangement and production to someone else. There's a loss of control there.

Still, it's hard to think of an artist with such an amazing body of work who has produced such a small collection of quotable remarks. (Her only rival in this regard might be Prince.) Here, to close, is one she gave me that's not bad as a encapsulation of the spirit of Kate Bush and her Never Never Pop.

"That's what all art's about – a sense of moving away from boundaries that you can't – in real-life. Like a dancer is always trying to fly, really - to do something that's just not possible. But you try to do as much as you can within those physical boundaries. All art is like that: a form of exploration, of making up stories. Writing, film, sculpture, music: it's all make-believe, really."

• Kate Bush plays the Eventim Apollo, Hammersmith, London, from 26 August to 1 October.