The leader of the Conservative group on Bristol City Council is calling for a vote of no confidence in First Bus.
Councillor Peter Abraham says the company's refusal to listen to passengers over timetable changes is the last straw.
First Bus says minor adjustments have been made - and it will review the situation in the next few months.
Laura Makin-Isherwood reports.
Supporters of Bristol getting its own elected Mayor have launched a campaign urging the public to vote in favour of the idea on May the 3rd.
The Yes group deny opponents' claims that a Mayor would add another level of bureaucracy to how the city is run.