You can discover Iceland like a local with the latest Stopover Buddy scheme... With airline workers

I inhale a lungful of crisp air and look upwards, sinking deeper into the warm water. Night has fallen, dusting the sky with stars, and the faint, green haze of the Northern Lights has smashed through it. Through their flickering light, candles illuminate my surroundings.

A 90-minute drive from the capital of Iceland, Reykjavik, the natural hot spring I sit in is a paddling pool-sized hole, surrounded by grassy clumps, dense snow and a smattering of trees. It's a prime place to see the aurora borealis, relaxing with a beer in hand, but I would never have discovered it by myself. And, judging by the fact that we're the only ones here, other visitors, many of whom are going to the country's best-known geothermal pools, including the Blue Lagoon, wouldn't do that either.

Many travelers want to get off the beaten track - but it takes local knowledge to find hidden spots like this, something that Icelandair is offering in its latest "Stopover Buddy" scheme. The idea is simple: transatlantic passengers en route to North America stopping in Reykjavik are matched with an airline staff member to serve up to 10 hours as their intimate, free tour guide.

Choosing from six themes (lifestyle, nature, fitness, community, food and adventure), from off-piste skiing with the CEO to sea fishing with cabin crew, you are matched with staff members specializing in this area.

Up to three people can be brought in, and when you pay for your own tasks, the airline takes up your buddy's expenses and pays them a day's rate for their time.

My friend is Siggi Anton, the 37-year-old website manager of the airline - and a part-time mountain rescuer - who built an exciting itinerary for me.

Not only did he drive me deep into the countryside to his favorite spring (the airline covers the cost of transportation to and from activities), he also brought everything I might have forgotten: towels to lie on the snow while dressing, local brewing gowns and bottles.

• In summer, Iceland: One family, one budget, and one luxurious getaway

• 5 Things to do in Iceland

• Due to spelling errors, visitors end up in the wrong region of Iceland

• Why did we form the Pirate Party and what would we do if we took power?

Buddies can also email tips for activities for you to do alone before meeting up, so I begin my two-day trip with the suggestion of Siggi - a sea swim at Nautholsvík geothermal beach. I watch the sun rise from a 39 ° C hot tub, joining a handful of locals - before slashing over frosty sand and tossing myself into the icy sea. I only last a few seconds, but leave a feeling of invigoration and readiness for the day.

Siggi suggested taking me on a 15km bike ride around the western region of Reykjavik, which, he says, is both picturesque and traffic-free, knowing I'm a keen cyclist. After meeting at Icelandair HQ, next to the domestic airport in Reykjavik, he drives us to Harpa, the futuristic concert hall on the harbourside, where our rental bikes are waiting.

Siggi says, clipping his hat, "The best way to see Iceland is by bike," "You see so much more than you do by walking. And unlike in a car, you experience it through all your senses, from the way it smells to how the air feels on your face."

Rolling up my balaclava to stave off the biting wind as we set off, under a cloudless winter sky, I'll soon understand what it means. As we roll past the Grandi harbour district, our tyres crunch through the snow, dotted with fishing boats and lined with a merry cluster of turquoise houses. Siggi states, "New York has the meatpacking district; this used to be our fish-packing district,"

These buildings - once fishermen's huts used to repair ships and nets - were turned into bars and restaurants. Slippbarinn, one of them, is equipped with cosy booths and comes alive at happy hour.

Another harbourside house, now home to the Valdis ice cream store, has a line of people pouring out. Even when temperatures like today are sub-zero, people are queuing for a taste of Danish liquorice ice, its trademark.

We are moving on with views across the sea to snowy mountains, heading towards the lighthouse on the westernmost islet of Reykjavik, Grotta. On the way, in a steaming hot pool over a flask of tea, we pass two women warming their feet and pause to peep inside a wooden shack where hunks of shark meat, reeking of ammonia, are hanging out to dry. It will later be sold alongside second-hand clothing, vacuum-packed lamb testicles and foal meat at Kolaportio, Iceland's biggest flea market.

We cycle around the headland, with its frozen golf course, with the afternoon sun now low, throwing pools of gold on the water, and back into the city along Aegisida, the waterfront street where Björk lives. As we are close to downtown, Siggi points to the grey house on the corner, home to Vigdis Finnbogadottir, the first female president of Europe. On 30 June 1980, after the results came in, she stood on her balcony waving to the thousands of supporters assembled to congratulate her.

I remember with a sense of satisfaction that all afternoon we did not pass another runner, let alone another tourist on two wheels. We go for dinner at Apotek, a centrally situated hotel and restaurant inside a former pharmacy, after having worked up an appetite. In the marble interior, elements of its old function are clear - there is a wall of drug bottles, while "pharmacists" mix drinks known as "painkillers", "stimulants" and "placebos" without alcohol.

The bustling restaurant fuses an Argentinian asado with Icelandic and European cuisine. Beautifully presented, the duck and waffle starter is an unusual combination of sweet caramel and meat, while the lamb rack is juicy. I wonder if there's a catch to what's basically a free tour guide service over chocolate pastries and scoops of rose-shaped sorbet.

It is currently subject to the availability of buddies (the books contain 50) and only runs until the end of April. But Siggi has other theories.

He says, "The idea is to give people a taste of Iceland," "The catch is that they'll want to come back."

Essentials for Travel

GETTING THERE Icelandair (icelandair.co.uk) flies to 16 North American airports from Gatwick, Heathrow, Manchester, Birmingham and Glasgow and, beginning in March, Aberdeen. Return fares start at 379 pounds.

VISITING THERE Without extra airfare, transatlantic passengers will stay in Iceland for up to seven nights. Visit icelandair.co.uk/stopover-buddy to order a stopover buddy.

MORE Details from inspiredbyiceland.com