'Come before the tourists visit" is the old Bangladesh tourist board slogan that had caught my eye and partially inspired my trip. Two days after arriving in the country, I unexpectedly meet the woman who came up with it. I'm at Wilderness, a resort in the north-eastern region of Sylhet, where the majority of British-Bangladeshis hail. It's owned by Nazim Choudhury, whose glamorous wife, Geeteara, now runs her own advertising company.

I tell them I'm heading to Cox's Bazar – the world's longest beach, on the country's east coast, and Geeteara says: "That's where I had the idea for the slogan. Walking on that beach in the 1980s, when no one was around."

"But," interjects Nazim, "the tourists, they never came!" He laughs, partly at the absurdity, partly because he is accustomed to expecting no different.

Domestic tourism, buoyed by a growing middle class, has been enough to keep his business going and, indeed, to help it grow. Wilderness is his second resort, and it has a slight treehouse feel, built into a hillside with an infinity pool amid the jackfruit and mango trees. Yet it sees few foreign guests.

"We've had one or two," he says. And I soon realise he is talking literally. Two, or maybe three, Brits have made it over the border from India – even though the Indian state of Meghalaya lies just half an hour away over the hills. I'd managed to make it all the way here on a direct flight from Heathrow. I skipped the chaos of crowded Dhaka in favour of a soft-landing at Osmani International airport, in the countryside just half an hour from Sylhet, the capital of the region of the same name.

The coast: south-east

Bangladesh's fledgling surf on Sonadia island, off Cox’s Bazar. Photograph: Nawaz Alamgir

Bangladesh is rarely considered a tourist destination. What people know of it generally comes from news reports: floods, cyclones, political strife, tragedies in garment factories.

"It has been stigmatised," says Yasmin Choudhury, who I am travelling with. "We never hear any positive news."

Yasmin was born and grew up in south-west London to Sylheti parents, but it's only since her father died suddenly in 2004 that she started to take real pride in her heritage. Now she's founded a company, Lovedesh, to overturn people's preconceptions (desh means country in Bengali, hence Bangladesh). Her aim is to showcase the best of the country, by offering escorted holidays, hosting wood-fired curry nights around the UK and promoting Bangladeshi fashion (which means traditional jamdani weaving, not H&M shirts).

I'm Yasmin's guinea pig – the first person she has taken to Bangladesh, apart from her 12-year-old daughter. Her aim is to try out places for her newly devised holiday itinerary. She's keen for my input, but it's hard to know where to start. One of the places I am initially undecided about is Cox's Bazar, a beach that stretches an incredible 125km down the eastern side of the Bay of Bengal. It sounds amazing, yet a number of Bangladeshis had advised me to skip it, calling it "overdeveloped" and "unimpressive". Even my guidebook is uncomplimentary: "World wonder it isn't." We decide to take a chance and travel south.

When we get to Cox's Bazar town, I can't help wondering if the naysayers are right. As the top domestic tourist destination, it's strewn with half-finished hotels – a muddle of high-rise, concrete blocks competing for a sea view. A fishy smell hangs in the air. When we climb into a tom-tom (as tuk-tuks are called here), our driver promptly crashes on a chaotic side street. It's hardly paradise.

But 10 minutes later, things take a turn for the better. The development around town is, indeed, a mess, but it's (currently) contained, which means you can leave the main parasol-strewn stretch behind and find yourself wandering the expansive shore, totally alone. It may not be bright-white sands and turquoise waters – the colour scheme is more beige and dusky blue – but it is wild, empty, pine-fringed and seemingly neverending. Later, we take a boat trip to Sonadia island, 9km away. We're the only people there – aside from a handful of fishermen, who live on the island year-round, drying fish in bamboo huts.

Back to her roots … Yasmin Choudhury, founder of Bangladesh specialist Lovedesh. Photograph: Nawaz Alamgir

It's similarly unexpected to find a burgeoning surf scene here. We're taken under the wing of the local surfing gang, who promise they'll have me standing up in my first lesson. One of them, Ramjan, explains how the first Bangladeshi surfer started here around 2002 when an Australian tourist left a board behind.

"With no wax and no leash, he kept falling off, but he managed to teach himself. We'd never seen anything like it, not even on TV. So we asked if we could learn too."

Ramjan has worked on the beach since he was a child: first selling eggs, then taking tourists' photos for a fee. He now helps support his elderly parents and extended family by working as a lifeguard (the RNLI came to offer lifesaving lessons a couple of years ago) and teaching surfing (£4 an hour). The Cox's Bazar surfers have also had a lot of support from a Hawaii-based organisation called Surfing the Nation, which has provided equipment and sponsored them to attend international contests. The boys are now passing on the goodwill by giving free classes to local kids, including a group of young girls who surf in hijabs.

It's another one of the gang, Rashed, who takes me out on my first-ever lesson. "Now stand up!" he calls on my second attempt, as the board rushes away from under me.

His confidence is misplaced, but it's encouraging and, after half an hour, I am doing a sort of wobbly crouch, which is satisfying enough. For beginners, the conditions are ideal. The water is warm; the waves are constant and not too rough. There are no wetsuits to hire, so I surf in leggings and a T-shirt – which also means I am not breaking any taboos.

This is the big challenge for Bangladesh: how to develop the natural asset that is Cox's Bazar? Not only does it have to keep those towering hotels and apartment blocks in check, it also needs to decide what sort of ethos to aim for. Currently, there are a couple of lively restaurants by the sea front, blaring out pop music and serving whole lobster for £6, but the virgin mojitos on the drinks menu are a reminder that this is a dry Muslim country. There are no beach bars, and no bikinis – though the idea has been mooted for a separate section of beach for those in revealing swimwear.

The forest: south-west

Bangladesh is one of the last places where fishermen still use trained otters to herd fish into nets. Photograph: Pierre Torset/Biosphoto

Leaving our surfer friends behind, we move on to Bangladesh's other major draw: the Sundarbans, the world's largest mangrove forest. On the map, you can clearly see the crisscrossing tributaries at the mouth of the Ganges making a fringe on the bottom of the country, and spilling across into India.

We book a boat trip with Pugmark , the longest-established operator in the region. Visitors would typically take a three- or four-day trip, staying overnight in the boat's basic but snug cabins. We only have a day. As we drift along the muddy waters, beside the low-rising, tangled foliage, we spot Ganges dolphins (like marine dolphins but with longer noses). Then, in a side stream, we run into some fishermen with a curious technique. To steer the fish into their nets, they use otters on leads. Loudly squeaking and squawking, the otters work in pairs to herd the fish.

"It's a dying tradition," one fisherman tells us. "It's hard to make a profit. I'm not sure we can do it for much longer."

Otters and dolphins aside, the main wildlife draw is, of course, the Bengal tigers. Around 500 live in the Sundarbans, but my expectations for seeing one are realistic – our guide has only ever had two sightings, each a two-second glimpse, right in the darkest depths of the forest). Nonetheless, when we moor to go for a walk, seeing a clear tiger footprint in the mud is thrilling enough.

As a precaution, we have a gun-wielding escort, Mizan. We ask him what the procedure is if he spots one. Clearly a frustrated thespian, he widens his eyes, hunches his back and jabs the rifle out, threateningly. He'd fire as a warning, he says, rather than to kill. The protection laws are strict, but the threat for people living here is real. In 15 years, Mizan has seen 45 critical injuries and 15 deaths caused by tigers. Local honey collectors are the most at risk, because the time they spend looking up at treetop hives gives the beasts ample opportunity to pounce.

Back on the boat, the crew lays out a huge spread for lunch: aloo bhorta (spicy mashed potato), parsha (a river fish, fried whole) and plenty of dahl. We also eat prawns, bought from the fisherman and whipped up into another quick curry by Yasmin. I imagine the supermarket label: "Non-farmed prawns. Otter-caught."

Our base for exploring the Sundarbans is a new resort, Panigram, near the town of Jessore, 43 miles north of the mangroves. Set amid luminous green paddy fields, it comprises a cluster of serene thatched bungalows besides a stream, covered in water hyacinth that is used to make biofuel. The location is very quiet and rural, and though it is still under construction, there is no chance of being disturbed by diggers. Everything here is being built by hand, with mud bricks, to keep the project both traditional and low-impact.

Community projects: north-east

Dusai Resort & Spa

Ambitious eco-resorts are a clear sign of confidence in Bangladesh as a tourist destination. In Sylhet, the Shuktara Nature Retreat (shuktararesort.com, doubles from £34 B&B) is a group of brick and glass-walled buildings designed by a local architect amid rolling hills. In the Srimangal tea-growing area further south in Sylhet, DuSai (dusairesorts.com, rooms from $120) is a grand resort that claims to be the first five-star offering outside of Dhaka. No doubt both also have their eyes on the Bangladeshi diaspora.

Yasmin also takes me to her ancestral village, Ali Nagor, close to where we started. It's surrounded by paddy fields and fishponds, and by the Surma river, on whose sandy banks children are playing cricket. It's where her father grew up and where, after founding a successful restaurant in the UK, he built a bungalow. It's shady and cool inside, with a wraparound veranda that receives a steady stream of visitors, from Yasmin's cousins to the local imam, who constantly flashes us big grins to reveal teeth stained from chewing paan (betel leaf combined with areca nut).

Yasmin puts together a potential itinerary for a place that has never seen a tourist: we're shown how to make wood-fire curry in a pit in the ground; we take a moonlit midnight walk; we go foraging; we take lilos to the river with the kids.

This part of the trip alone would have been reason enough for coming. One night around the bonfire, we talk about how the country has exceeded all our expectations. Our photographer, Nawaz, also British-Bangladeshi, has been in a constant state of disbelief.

He admits he had "zero interest" in the country before this trip, but is now planning to return with friends. Yasmin says the hardest market to convince is second-generation British Bangladeshis, who associate the country with childhood trips, being traipsed round the houses of various relatives, torn away from usual home comforts.

Travelling in Bangladesh is not all rosy – the driving is terrifying, the infrastructure is limited and strikes, like those that greeted the elections in the early part of this year, can bring things grinding to a halt. It will be a bumpy journey for the tourism pioneers, but their ambitions are not groundless. Beyond the headlines, there's another Bangladesh out there and it feels like it could be on the cusp of a new era.

Getting there

Flights were provided by Biman (biman-airlines.com), which flies from Heathrow to Sylhet from £470 return. Internal flights with United Airways (uabdl.com) cost from £30 one way

How to do it

The trip was provided by Lovedesh (020-3290 7768, lovedesh.com), which creates bespoke trips to Bangladesh from £1,400 for 7 days excluding flights*. Lovedesh's Yasmin Choudhury also works with Wild Frontiers (020-7736 3968, wildfrontierstravel.com), which offers 16-day escorted trips to the country in October 2014 and February 2015, from £2,695pp, excluding international flights*

Where to stay

Ahead of its official opening later this year, the Panigram eco-resort (panigram.com) is offering cut-price stays (from £95 a night) at the unfinished site. The Wilderness in Sylhet has rooms from £72 (+88 173 071 2600, nazimgarh.com). At Cox's Bazar, two-night full-board stay at Ocean Paradise hotel (oceanparadisehotel.com) costs from £107

* The prices of the trips in the fact box have been updated twice since the article went to print on 3 July; the original prices quoted by the tour operator were incorrect