Ruth Hubbard, of the It’s Our City campaign, criticised former council leader Julie Dore at a full council meeting.
Ms Hubbard said last November, a member of the public presented a petition but was “attacked” by Coun Dore.
Labour said the member of the public was actually a Liberal Democrat candidate trying to “weaponise” local issues.
Ms Hubbard said: “Coun Dore responded to a member of the public presenting a petition about free school meals by delivering a quite extraordinary attack. She was egged on by at least one other member of the ruling group.
“Whilst this was not the first time the former leader was rude or aggressive in responding to members of the public, the attempt to belittle and humiliate this member of the public was particularly nasty and bullying.
“Many members of the public are nervous before asking questions because the former leader was known for responding in a hostile way.
“The ante room at the Town Hall before full council, where public questioners are asked to gather, was frequently something of a support group for members of the public because they knew what might be coming.
“The former leader was called out by two public questioners for her behaviour. What action did the monitoring officer take in response to this bullying?”
Coun Dore was at the meeting but new council leader Bob Johnson responded on her behalf.
He said he welcomed public questions but added: “This is a space for legitimate public concerns and should be free of cynical political opportunism.
“Councillors made the commitment to provide free school meals to children over the Christmas break and the Liberal Democrats were aware of this yet their candidate presented a petition to try and make political capital.
“It was not constructive opposition, but an attempt to get political mileage by posing as a legitimate public question.
“This is why I believe Coun Dore responded with such annoyance to this disingenuous petition from a Lib Dem candidate. Free school meals should not be weaponised for political point scoring.”