THERE it was. A young brown bear, padding through the sunny wildflower meadow looking for lunch. We watched from our hillside vantage as this small, deceptively cuddly looking creature foraged in the long grass. Then it stopped and raised its head. Had it seen us and the growing number of other roadside watchers? Time to get back to our RV before we were lunch.

In the safety of our home on wheels — RV stands for “recreational vehicle” — we made a sandwich for the road and headed off for some more wildlife adventures, Wyoming-style. We had gone to Yellowstone National Park to see the wonders of its landscapes, erupting geysers, canyons and waterfalls, pine forests and plains where bison roam.

That night we pulled up at a Yellowstone Park Service campground and picked a wooded spot near the river. As the sun went down, we floated in its gentle currents, warmed by hot springs, and watched a herd of elk grazing on the bank. It couldn’t get any better.

Back at the campsite, our neighbours were cooking dinner on barbecues or campfire pits. The grown-ups drank beer and swapped bear stories while the children played their last woodland game of the night.

The highlight of the day for our daughters Amalie, 6, and Josie, 4, was toasting marshmallows on the campfire before climbing into their pull-down bunk bed and peeking out through the curtains by torchlight.

The joy of an RV is that, because you take everything with you on your road trip, there is none of the endless packing and unpacking that comes with a tent or hotel accommodation. And it feels like a special kind of freedom.

Everything you need is right there — kitchen, bedroom and bathroom. But be prepared for your 7.5m (25ft) van to vibrate, and for deafening rattling on a bumpy road.

And the maddening line “when are we going to get there?” doesn’t come nearly so often when the children can draw, play games, or watch a video while you are driving.

This was the typical scene at sun-up: the girls sat strapped in at their table seats still in their pyjamas, clutching their hot chocolate and whooping every time we went over a bump. These dawn dashes, with only bison crossing the road to delay us, meant we could beat the July crowds at Yellowstone’s big tourist pulls.We saw the Old Faithful geyser shoot 40m (130ft) into the air before most people had emerged from their hotel door.

That freedom to take off whenever you want is one of the main reasons that seven million households in the US own an RV. Although the National Park Service campgrounds have the most beautiful locations and spacious sites, seasoned RVers prefer the extra facilities that independent and KOA (Kampgrounds of America) sites offer.

Here you will learn the intricacies of hooking up for power and water. And every few days you have to face the inevitable. The snapping on of rubber gloves to hook the sewage pipe to the dumping station sent our daughters running for cover shouting “euwy!”

Picture the scene at one such campground at the foot of the snow-capped Grand Tetons near Yellowstone, as an old-timer supervised our first such whiffy experience.

It’s dusk and the outdoor pool is slowly emptying. The teenage girls are finally out of the showers, the “moms” have left the steamy launderette. The steaks are sizzling at the campsite “cook-out” café. Men in baseball caps are swapping fishing tales around the campfires and grannies sit in deckchairs under fairy lights. Dogs bark and country music plays.

Of course no trip out West is complete without meeting a real cowboy. Ours was called Ryan, a gruff giant of a man who kept a 200-horse Wyoming ranch by day and gave the likes of us wagon rides in the evening.

He wore Wrangler jeans, checked shirt, cowboy hat and cowboy boots but insisted: “I don’t just dress like this for you . . . I’m a modern cowboy, I drink beer, watch TV and use a computer.”

His son Braydon, 5, was a cowboy in training, introducing his new British girlfriends to the horses, and inviting them back to the ranch.

So we’d met the cowboys. Now for the Indians.

Just east of Glacier National Park, near Montana’s border with Canada, members of the Blackfeet tribe perform haunting music and ceremonial dances for visitors. A local elder, the town lawyer by day, told tales of hapless hikers armed with pepper spray and jingling bells against bears. It turned out that Josie’s tactic of making human noise whenever in bear country — in her case singing Zip-A-Dee-Doo-Dah — was the approved way.

Then the Blackfeet invited us to join in the “round dance”. A hundred people of all ages, from all over the world, linked hands and circling the whole building to the beat of the drums.

The next day we set out to camp among the park’s cedar and hemlock forests and swim and canoe in the lakes, sharing the beaches with just a few other families.

But to pass the narrow hairpins of the Blackfeet-named “Going to the Sun Road” through the mountains we had to leave the RV at the campsite and take the hiker shuttle bus. Then for the highlight of Amalie’s trip. A short climb through a wildflower meadow in 32C (90F) heat chasing a yellow-bellied marmot (it looks a bit like a beaver) to play on a plateau of perfect snow where mountain goats roamed.

“This is so cool,” she said. “Can I have my chocolate for being a good walker now?”

NEED TO KNOW

Getting there: In mid-June, Trailfinders (0845 0585858, www.trailfinders.com) offers Northwest Airlines flights from Gatwick to Billings, Montana, from £531 per adult, £377 per child under 12. The Recreational Vehicle Rental Association (001 703 591 7130, www.rvra.org) lists dealers by state. Prices are about £380-£670 a week.

UK RV rental: Hemmingways (0870 7422673, www.hemmingways.co.uk) offers RVs from £86 a night when you pick up in Salt Lake City for Yellowstone.

Where to stay: Reserve RV pitches through the National Park Service (001 301 722 1257, www.reservations.nps.gov). Some sites operate a first-come, first-served policy.

Yellowstone National Park (307 344 7381, www.nps.gov/yell): £11 weekly fee, camping £10-£18 a night. Glacier National Park (406 888 7800, www.nps.gov/glac), £5.50 weekly fee, camping £9 a night. KOA Kampgrounds (406 248 7444, www.koakampgrounds.com), £17-£32 a night.

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