The Perth-based company said a rise in fares helped boost like-for-like revenues on its regional bus routes by four per cent compared to last year in the 12 weeks to July 20.
Passenger numbers rose 0.9 per cent in this period.
Stagecoach said revenues from concessions and school contracts were also growing, though many local authorities across the UK have reduced subsidies for bus services in recent years, leading to the closure of some routes.
In London, where the firm has 1,300 buses, revenues rose 14.4 per cent as several new contracts came into effect.
However, Stagecoach noted that frequent roadworks along its routes had caused delays and reduced the amount of "quality incentive income" it receives from Transport for London.
The company intends to bid for new and existing bus routes in London, and aims to boost commercial revenues in the rest of the UK.
Rival operator First Group last month reported a 2.7 per cent rise in UK bus passenger revenues in the three months to the end of June and said it was "rebasing" its fares and routes. First issued a profit warning in 2012 after the UK Government cut subsidies to bus operators.
Stagecoach's rail business, meanwhile, yesterday reported a 4.9 per cent rise in revenues compared to a year ago. The firm said it was keeping a close eye on costs to offset the rising payments it must make to the government for running the South West and East Midlands routes.
The firm, led by Martin Griffiths and chaired by Sir Brian Souter, said its rail staff "continue to discuss" extending these two franchises, though it does not expect the awards to be made official until after the general election in May 2015.
Despite losing out on a contract to run the Docklands Light Railway franchise in London last month, the firm said it was "optimistic" about the prospects for its rail business. Stagecoach, First Group and a Go-Ahead joint venture have been shortlisted to take over the Transpennine Express franchise.
Stagecoach's joint venture with Virgin is also on the shortlist to take control of the East Coast Main Line next February.
The venture recently won the right to run the West Coast Main Line until at least March 2017. Revenues from the route rose 5.7 per cent in the last quarter.
The government's decision to hand the East Coast back to a private sector operator, following National Express's abrupt withdrawal from the line in 2009, has been attacked by transport unions and the Labour party.
"Although there are a number of challenges to growing profit in the year ending 30 April 2015, overall current trading is satisfactory and we remain on course to meet our expectations for the year," Stagecoach said in its trading update.
Joe Spooner, an equity analyst at investment bank Jefferies, said yesterday's comments from Stagecoach "reflect a very consistent update across the trading units. Given the steer and trading performance, we do not expect any material change to consensus."
In North America, Stagecoach reported a 4.9 per cent rise in revenue. This was driven by the firm's fast-growing Megabus inter-city coach business, which brought in 14.9 per cent more revenues than a year ago, aided by new routes in Florida.
Its Twin America sightseeing buses are faring less well, with the venture still in talks with the US Department of Justice to resolve a competition lawsuit.
"The New York sightseeing market remains highly competitive, with current trading challenging," the firm said yesterday.
London-listed shares in Stagecoach rose 5.7p, or 1.6 per cent, to close at 365.2p.