Shares in Stagecoach climbed 2.7%, or 9p, to 343.2p yesterday on the back of the solid trading update.
Stagecoach, meanwhile, reiterated its interest in considering a bid, along with partner Virgin, for the East Coast Main Line franchise.
The UK Government last week published the prospectus for East Coast, which is currently being run in the public sector.
Stagecoach said yesterday that like for like revenues in the 24 weeks to October 13 in its UK bus business, outside London, were up 5% on the same period of last year, with year-on-year growth having accelerated in the latter 12 weeks of this period.
A Stagecoach spokesman noted this growth had been achieved in spite of reductions by local authorities in tendered services. Such socially necessary but otherwise uneconomic operations include bus services in areas in which passenger numbers are low or at times of day when there is less demand.
The spokesman said: "(In) the past 18 months, I would say I have seen a pattern (of) ...austerity measures that have affected the public sector flowing through into local authorities reducing the level of tendered bus services in their local areas."
He added: "Our core commercial bus networks...have remained strong and (are) getting good growth in full-fare passenger volumes."
Like for like revenues of Stagecoach's North American business in the five months to September 30 were up by 7.3% on the same period last year. Perth-based Stagecoach, chaired by co-founder Sir Brian Souter, said its Megabus coach business in North America was the fastest-growing part of the group.
The revenue of Megabus in North America in the five months to September 30 was up 23.7% on the same period of last year, reflecting growth in existing services and contributions from networks in Texas and California which were launched in the 2012/13 financial year.
Stagecoach said that, overall, its North American business remained on track to deliver a "significant increase" in operating profit in the year to April 30, 2014, compared with 2012/13.
Virgin and Stagecoach are partners on the West Coast Main Line rail franchise. Their Virgin Rail Group joint venture continues to earn a fee equivalent to 1% of revenue from the West Coast franchise, with the Department for Transport taking the risk that revenue and/or costs differ from those expected.
Like for like revenues in the 24 weeks to October 13 at Stagecoach's own UK rail business, which takes in South Western Trains and East Midlands Trains, were up 3% on a year earlier.
Stagecoach bid last month to run the Docklands Light Railway in London. It is also working on a bid for Thameslink. Winning bidders for these franchises are due to be announced next spring.
Stagecoach said its overall profitability had remained satisfactory, with "no significant change" to its expected adjusted earnings per share for the year to April 30, 2014.
The City has been forecasting Stagecoach will make pre-tax profits of £181.8m and earnings per share of 24.8p in the 12 months to April 30, excluding exceptional items and intangible asset expenses, up from £177.4m and 24.6p respectively in 2012/13.