Trade union Unite said the operator is refusing to offer more than 560 workers at depots a reasonable pay rise.
Unite general secretary Sharon Graham said: “Bosses at Stagecoach’s Yorkshire Traction Company should know that Unite is ready for a relentless campaign if members vote for strike action.
“Unite members all over the UK are taking action right now over Stagecoach’s penny pinching on pay.
“Stagecoach’s board should be in no doubt that Unite is wholly dedicated to advancing the jobs, pay and conditions of our members.”
Despite the Covid-19 pandemic, Stagecoach’s latest accounts reveal that the group made a profit of £58.4m in the last financial year.
The ballot for strike action opened today and closes on November 8 and, if members vote for industrial action, strikes could begin as soon as next month.
Unite regional officer Phil Bown added: “Our members are the lowest-paid bus workers in the region.
“They rejected Stagecoach’s latest derisory pay offer by 97 per cent on a turnout of 90 per cent - this shows that a vote for strike action is highly likely.
“If passengers face serious disruption this winter, it will be entirely Stagecoach’s fault.”
It comes after Stagecoach announced driver shortages will see dozens of bus services culled across Barnsley at the end of the month.
“Along with many other industries, bus operators across the country are experiencing a shortage of staff,” a spokesperson said.
“This leaves the company with not enough drivers to run all journeys each day and though our teams have worked incredibly hard, sadly we’ve had to cancel some journeys, sometimes at short notice.”