The Perth-based company, which has operations in the UK and North America, reported a 0.9% rise in bus passenger volumes outside London in the 12 weeks to July 20.
Across the group, Stagecoach described overall trading as satisfactory after revenues from UK rail operations including South West Trains and East Midlands Trains rose 4.9%. Its North America division posted the same rate of growth amid the continued expansion of its megabus.com service.
Around 2.8 million passenger journeys are currently made on Stagecoach buses each day, including in Liverpool, Newcastle, Hull and Manchester.
It recently placed orders worth more than £90 million on new greener buses for 2014/15, with the company highlighting its confidence in "continuing to get people out of their cars and back on board the bus".
Stagecoach said revenues earned directly from fare-paying passengers contributed most to the bus division's 4% growth rate, with concessionary, contract, tendered and school revenues also continuing to grow despite efforts by local authorities to minimise concessionary reimbursements.
Stagecoach's other UK operations include budget coach service megabus and the rail networks South West Trains, Island Line and East Midlands Trains. It has a 49% shareholding in Virgin Rail, which runs the West Coast franchise.