The Stagecoach East staff took the stance after bosses tabled a new offer.
The company offered workers at bus depots in Fife a 2.4% pay rise backdated to the start of May.
Members of the Unite union accepted it marked “a step forward” but said it fell short of its demand for a “fair” pay claim of the Retail Price Index inflation figure 3.8% at July) plus 1% .
Around 500 members supported strike action with Fife workers supporting it by 93% in a 74% turn-out.
Similar responses were recorded in the other two regions affected.
The workers involved in the dispute are drivers, engineering and administrative staff, and cleaners.
Any industrial action could impact on the forthcoming COP26 summit in Glasgow .
Dougie Maguire, Unite regional coordinator, said: “The strength of resolve is crystal clear for all to see.
“There needs to be some perspective in this dispute because while Stagecoach East has made a new offer, which is a step forward, there is still some distance to go.
“It falls far short of our members’ reasonable and fair pay aspirations because we are dealing with an extremely profitable company.”
He said the union’s aim was to reach an amicable settlement without strike action, but added: “The public need to know that Stagecoach East has turned up to this dispute well over the expected time of arrival.
“Unite’s members have been left with no option but to consider walking because the company hasn’t done enough talking.
“ If Stagecoach decides it wants to talk then Unite is willing and waiting, but only if it turns up with a fair offer.”
The bus company said it would “leave no stone unturned” in an attempt to reach a settlement.
Its offer includes new start drivers reaching full pay rate six months earlier, and a commitment to a further pay review for east Scotland employees in May 2022
It said the 2.4% offer to staff at depots in Dunfermline, Glenrothes, Leven and St Andrews would see them get up to £633.33 more per year.
And it called on the union to “put communities first, and talk not walk”
David Frenz, operations director at Stagecoach East Scotland, said: "Buses are a lifeline for local people in Fife.
“We are committed to ensuring our people who keep our communities connected are properly rewarded, particularly after their contribution to the country over the past 18 months of the pandemic.
“We have worked tirelessly to protect the jobs of our people during the pandemic and done everything we reasonably can to hold constructive discussions with Unite to reach a sensible and sustainable pay agreement across our bus depots in Fife.
“We are leaving no stone unturned in a bid to reach a settlement.
"That is why we have put a fresh pay offer to Unite which would give employees a 2.4% pay increase.”
Stagecoach said services are facing a “continuing challenging financial environment” with passenger levels significantly down on pre-Covid levels.