I went to US state with 125 billionaires — I've never seen so many private jets

The guide was pretty clear: "Keep both hands on the handlebars. Don't look around. Don't take photos."

But I couldn't help myself. It was all too beautiful and I just had to shoot videos of the magnificent alpine landscape surrounding us while freewheeling down from the Maroon Bells, the twin peaks behind the twin towns of Aspen and Snowmass, their snowy caps still clinging to the last vestiges of winter despite it being late June.

This part of the Rocky Mountains of Colorado is better known for its skiing and winter activities, yet in summer becomes a playground for those who like to explore the land no longer hidden by white stuff.

I'd flown in from Denver, leaving the state capital basking in the evening sunshine as we drifted over the snow-stained mountains. Rows of private jets lined the runway of little Aspen airport. I'd never seen so many. Then again, this is one of the most affluent areas in the US, with up to 125 billionaires owning property. Visitors seem to be mostly rich or "aspirational". Think south of France or Dubai, but with cowboys.

Our hotel was the cool W, at the centre of Aspen and close to the cable car station. It was as modern and trendy as the other Ws I've visited, yet smaller in scale – less flash, more cosy. After freshening up, I joined my tour group on the rooftop bar where we quaffed cocktails as the sun set with golden rays kissing Mount Aspen.

Drinks drained, we set off for dinner through the quaint, leafy streets of Aspen, which show few traces of its gritty past as a silver mining town. After the silver boom was over, Aspen's fortunes sank and only recovered after being developed into a ski resort in the mid-20th century. I noticed I was having a little difficulty walking. The alcohol? No, the 8,000ft altitude (the thin mountain air would render me short of breath for the next few days).

The atmospheric Steakhouse No. 316 was dimly lit with cool Old West chic decor. My fillet steak was cooked to medium-rare perfection and washed down with a spicy margarita.

Pesky jetlag ended the frivolities, knocking me out by 11pm, then pinging me awake at 3.30am. At least it meant I was first to breakfast. I had elk sausage and eggs – my first taste of the majestic beasts that still roam the region – strong, smoky, and as tasty as they are handsome. Poor elk.

The morning's activities included e-biking up the valley via pretty wetlands (the power-assisted pedalling a godsend) and a visit to the cool Aspen Art Museum, with its six galleries of contemporary art.

We lunched at the museum's rooftop restaurant. Its food may have been bland, but the view of Mount Aspen was as breathtaking as the stairs up there.

All the locals we passed or met that day were ridiculously friendly, giving way to us with wide smiles or happy hellos. Despite Aspen being so upmarket, it had none of the haughtiness you might expect in similar British or European resorts.

Post-lunch, we perused souvenir shops. The highlight was Kemo Sabe, a Western-themed store selling custom cowboy clobber. It's as expensive as it is cool – hats averaged $1,000. I saw a simple leather hatband for $8,776. Surely, no one's that aspirational?

Keeping the Western theme, dinner was at Hotel Jerome, a grand building constructed in the 19th century as a rival to London's Savoy. Its bars and restaurants exuded a more mild West charm, though the seven-course tasting menu was sadly lacking. Still, the cocktails were excellent and the history palpable.

The grandness continued as we ambled to the nearby Wheeler Opera House for an Emmylou Harris concert. I'd never heard of her, and the 77-year-old, 14 Grammy-winning folk singer put my ignorance to shame as her mesmeric voice resonated around the handsome Victorian-era hall.

After another night of jetlag-curtailed sleep, I was pleased we took a cable car to the summit of Mount Aspen for an open-air yoga class where I stretched out my tired limbs overlooking the mountains.

Lunch was back down at the Ajax Tavern next to the cable-car station. Its signature truffle fries were fantastic, but the signature double beef burgers were quite average.

That sunny evening we moved on to Snowmass, 15 minutes down the valley, stopping at the rodeo. But this wasn't just any rodeo, this was the Snowmass Rodeo – with lots of well-Cuban-heeled cowboys and girls sporting Kemo Sabe hats and designer sunglasses. Still, it felt down-to-earth, with perky families and smiles all around. Events were a mix of children's sheep-riding (yes, really), bullock lassoing and barrel-racing, culminating in bull-riding.

Snowmass Village itself has a different vibe from Aspen. Here, the resort is built around the skiing – and not vice versa – with a network of trails and pistes fanning up the massive Snowmass Mountain.

In summer, the forested slopes are a mountain biker's paradise, with more than 50 miles of trails. As we rode the gondola up the Elk Camp side of the mountain, we watched as they bombed down, churning up trails. Fun, but we got our thrills from the Breathtaker Alpine Coaster, a roller coaster in the forest where you speed downhill in toboggans, my bum squeaking as loudly as the brakes.

From the cable-car terminal, there's a chairlift up to the summit of Elk Camp. Sadly, it was cold and rainy up there and the views of the Maroon Bells obscured by cloud.

A pit stop for pizza fuelled us for the descent into Aspen's tree woods above the village. The afternoon sun struck their silver bark and cast long shadows. What with the birdsong and after-the-rain aromas, it felt magical.

Snowmass's nightlife is more subdued than Aspen's. We dined at Aurum, an upmarket Mediterranean/American fusion restaurant – more great steak and cocktails – and also at Kenichi, a Japanese spot with not only the best food of the trip, but the best Japanese food I've ever tasted.

Zane's and The Tavern are popular pubs – the former a low-key sports bar, the latter packed with rowdy young revellers drowning out the croaky old country singer.

Our final morning began with that bike ride down from Maroon Bells. The view of the twin peaks towering over the pristine Maroon Lake was a most spectacular sight. And, mercifully, the ride back to Aspen was downhill all the way.

After such a breathtaking trip, in both senses, it was a fitting finale.