Madrid, Montreal, Melbourne, Martinique, and, of course, Malton.

Yorkshire Coastliner has some some surprising connections beyond the A64 and local diversions. The fleet of blue double-deckers, with their breaking wave logo, is part of a worldwide public transport empire that can seem an unlikely concept when they're avoiding sheep at Goathland, calling at Scagglethorpe, or delivering Tony Lightfoot to his caravan at Filey.

The bus he catches to the seaside is now owned, along with trains, trams, metro systems, coaches and ferries in more than 20 countries, by a company called Transdev, with a boardroom in Paris.

For the pensioner, it is just one more surprise of modern life. Another is the fact that he can travel free on Coastliner at almost any time of the day. Being issued a ticket stamped "no fare paid" makes the journey even more pleasurable.

"I always go upstairs because you always see something different, things you don't see from the train or a car. It's like you're peeping over the hedges and seeing farms and grand houses for the first time. There's a lovely view of Castle Howard from the top deck and all the wildlife that I didn't notice before.

"The other week, our driver got wind of congestion ahead on the A64 so he doubled back and we took back-roads through Kirkham Abbey. Absolutely beautiful," said Tony.

"The only thing is, it's such a grand service there are times when it's a victim of its own success. I go from York to Filey on a Friday to get the caravan ready for the weekend and the wife follows on Saturday. On a few occasions recently she's had to stand part of the way."

Aren't longer journey times another disadvantage? It can take nearly three hours from Leeds to Scarborough by Coastliner compared with 78 minutes by train. "I'm not in the fast lane any more," said Tony. "When you have all the time in the world, that doesn't matter."

On the 840 service, which departed York station for Whitby at 10.22, bang on the timetable schedule, 86-year-old Joan Sadler – "that's Miss!" – agreed. She travels on Coastliner at least once a month, summer and winter, "and I used it when you had to pay. It's a lovely run across the moors and I'm particularly fond of this service. It's not the express, so we stop at one or two villages and get to Whitby just in time for lunch.

"I have my little rituals there – a bite to eat at Botham's, then a scoot round the charity shops, a quick look at the sea and back on the 3.06. My one regret is that I can't make it upstairs now. Everyone tells me the views are marvellous from up there." They are. The Hole of Horcum is deeper still from up top and you glimpse the sea a fraction sooner than other vehicles on the A169.

Paul Amey missed that because he got off in the dip at Eller Beck. He's a member of the Yorkshire Wildlife Trust and was visiting a moorland nature reserve.

He was also something of a rare bird himself on the mid-morning Coastliner: a fare-paying passenger. He's six years away from being entitled to free off-peak bus travel, so paid £9 return from York, plus his train fare to the city from his home in Harrogate.

He has never had a driving lesson and public transport is his lifeline. "It's better than a lot of people think. With careful planning you can get to some fairly remote places. Trouble is, you end up becoming a walking timetable."

For companies like Coastliner, a combination of Government policies and global economics have created a surge in business which was growing even before the National Concessionary Travel Scheme in England for the over-60s and "eligible disabled" was extended on
April 1 to include services outside a permit-holder's home area.

It's coincided with soaring fuel costs impacting on transport, public and private. The environmental plus-side is that bus operators are now attracting more car owners, especially the over-60s. The reason is obvious. If journey times and convenience aren't major considerations, why spend money on petrol and parking when you can travel free?

Retired teacher Elizabeth Smith, from York, and her 71-year-old friend, Mike Heddon, who lives in Bradford, are both converts to Coastliner.

"We've become huge fans of the service," said Elizabeth, one of 32 mainly elderly passengers upstairs, en-route back from Whitby. "The journey from up here is a delight. I particularly love it when we leave the main road at the Fox and Rabbit Inn and drop into Thornton Dale through a tunnel of trees, and the branches are brushing the windows. Now that we've discovered it, we'll also take the bus to Scarborough for the cricket.

"If part of the idea behind this scheme is to get people out of their cars, then it's succeeding in our case. Mine has hardly been out of the garage recently. Free travel on the bus is the answer for us, except that I wouldn't want to try bringing my cello on board."

In 2007, there were 1.5 million passenger journeys on Coastliner, a 15 per cent increase on the previous year. Business is increasing to such an extent that the company has abandoned single-deckers and invested in an all double-deck fleet of 22 to provide extra capacity. When a new vehicle costs £240,000, the dilemma for managing director Dave Alexander is trying to gauge how much new business is out there to justify buying more.

Despite the upward trend, does the increase reflect a lasting shift back to the bus, or is it a response to the novelty of free transport and a short-term reaction against the hike in petrol prices?

Alexander says that it's too early to judge. It's an unpredictable business, and, to some extent, seasonal. "On a warm, sunny day we can be overwhelmed by passengers wanting to go to the coast or countryside. Our staff have become expert at understanding travel patterns."

The Government and local authorities are trying to work out how best to reimburse bus operators now that 11 million people in England are entitled to concessionary travel on local services throughout the country.

At present, payments are based on a complicated system of calculations which vary from area to area. There is every chance that additional funding of £212m, provided by the Department for Transport to finance the concession, has underestimated the demand.

One driver estimates that at certain times of the day, 75 per cent of his passengers are travelling free, if you ignore their contribution as taxpayers. "I don't begrudge them. They've paid their dues."

At other times, Coastliner is a means of getting to work and college. There's no doubting a journey's variety, scenic and otherwise. One route calls at a psychiatric unit, science laboratories, Flamingo Land, and Heartbeat country.

Alexander points out that the service is "different things to different people. We carry commuters, families, tourists, pensioners, students, those who use it for local journeys and others who regard it more as a coach service than a bus service. We have to try to cater for everyone."

It's one reason information screens, describing points of interest en-route and attractions at destinations, are being installed in the fleet. "We are looking at what airlines do for in-flight entertainment and how we might apply some of their ideas.

"The feedback we get, especially from leisure-users who don't have time constraints, is that the bus journey is part of the experience of their day out. It starts when they get on board. It's less stressful than driving yourself and cost is an increasing factor. People are beginning to leave their cars, me included."

Rising fuel prices are a double-edged sword for Coastliner. The company is already paying 70 per cent more than a year ago, "but so too are motorists. If escalating costs begin to mean less
traffic on our main route, the A64 corridor, that can translate into extra business for us and further improve the service's reliability.

"It's possibly a new era for the bus. These things take time to filter through the system, but if you're spending £20-£30 a week more on petrol, and start to do
the sums, public transport begins to look very attractive."

That's certainly the view of Ken and Shirley Woolley, from Burton-upon-Trent. After an early breakfast they'd travelled to Malton by train, using their Senior Railcard, and then caught the Coastliner to Whitby, courtesy of a bus concession pass issued by their council in Staffordshire. They were considering a return journey via Scarborough, or maybe even going by way of Saltburn and Middlesbrough.

"The flexibility of the scheme is marvellous, and it's liberating thousands of us. For our generation, the bus has become almost a social service.

"We still have the car but why use it when we can travel all over, and often for nothing? It's reaching the stage where we need it for the supermarket run and that's about all."

For information about Coastliner services: 01653 692556 or 0113 244 8976, www.coastliner.co.uk