It is well known that there were no Harley-Davidsons in Ireland until The Late Late Show. Then, on the night of his final programme, in May 1999, Gay Byrne, who was a few months from turning 65, was given one by Bono and Larry Mullen, of U2. "It's a very Elvis thing for us to do," Bono remarked as the audience applauded.

There is indeed something very Elvis about a Harley. Something quintessentially American.

Jeff Murphy's Dublin Harley-Davidson dealership, at Red Cow Retail Park on Turnpike Road, oozes the USA. And it oozes cool. There's so much chrome you nearly need sunglasses. There's leather, too, lots of leather, and check shirts and jeans and cowboy-style boots. Harley's distinctive black and orange corporate livery is everywhere.

Within a few minutes I am on the M50, cruising down the outer lane on a Harley Heritage Softail, 1,690cc of big Harley engine throbbing under me, exhausts rasping out that deep, pleasing, slightly dull Harley hum that says, “Power!”

Last Sunday a group of men and women (Harley is gender-blind) gather ahead of their weekly run at a petrol station on Naas Road. About 30 of the 175 members of the Harley Owners Group (Hog), Gaelic Chapter Ireland (average age: mid 50s) are there for a scoot up to Co Fermanagh.

First to arrive is Val from Lucan on her Electra Glide Ultra Classic, a vast machine that seems to combine languorous luxury with a low, growling power waiting to be unleashed. It is, basically, a flying armchair. Val lights a cheroot, walks away from the bike and, with an unrestrained laugh, expresses the hope that she doesn’t let the thing topple over anytime I’m looking.

Next in is Therese on her Sportster 883. She is straight out of Harley central casting. She’s tanned and wears shades, a tank top and leather trousers.

Within minutes the station forecourt is throbbing as the fleet of Softails, Ultra Classics, Road Kings and several other types of Harley head out, led by Therese’s husband, Derek Smith, who is the floor manager of the Harley dealership and captain of the lead seven bikes of the Fermanagh-bound posse.

The countryside glides by. Hands firmly gripping the bullhorn handlebars, you sit low in the fat, wide, comfortable seat, ease your back against the rear support and raise your feet on to the cruising pegs.

Now, in your own little Harley bubble, you own the road.

Harleys – most of them anyway – lend themselves to cruising, especially the Fat Boy, the Heritage series, the Ultra Glides and Road Kings.

At Lusty Beg Island, on the north shore of Lower Lough Erne, the riders lean on a fence after lunch, peering across the water at the cabin cruisers and hyperactive teenagers jumping in and out of the water.

I ask some of the Gaelic Chapter members to explain the appeal of the bikes.

“The sociability,” says Therese, “and they’re such icons.”

“We fell in love with them in the States,” say Charlie and Margaret from Dublin, riders of a Road King Classic. “The look, the sound, the laid-back, easy-going attitude that revolves around them.”

Before today Cait from Dublin had never been on a bike – any bike – but came as pillion passenger with one of her film-production-company colleagues. “It’s pretty fantastic,” she says. “It does feel like you own the road. Other road users have a bit of respect if you are on a Harley.”

Gay Byrne was a bike fanatic most of his life, watching road racers as a boy on the Isle of Man, around Skerries, in north Co Dublin, and in Co Wicklow. He flogged his Harley for charity in 2003 and then got himself a Honda Deauville. He offloaded that recently.

He’s 78 now. “I’m in the market for a bike again,” he says.

Good grief, will the lad ever grow up? Hope not.

Peter Murtagh's Heritage Softail was loaned by Harley-Davidson Dublin to mark the manufacturer's 110th-anniversary celebrations, which include a current Irish Times competition to win a Harley-Davidson Iron 883.