The drivers – Unite members – are balloting for strike action over pay because earning less than £11 an hour, they are being paid less than drivers working in Gloucester and Cheltenham.
Labour councillors hope industrial action can be avoided if the employer does the decent thing and agrees to pay parity.
Cllr Doina Cornell said: “We fully support these highly-skilled drivers in their campaign for fair pay. They have worked throughout the pandemic under difficult and stressful circumstances. We’re calling on Stagecoach management to reward them with a decent wage and avoid industrial action that will affect people living in Stroud district.”