Former minister Crispin Blunt took aim at the Speaker in the Commons, although Mr Bercow was not in his seat to respond.
Earlier, in response to a point of order from shadow sport minister Rosena Allin-Khan, Mr Bercow condemned racist abuse aimed at England footballers during their 5-1 win against Montenegro.
Mr Blunt welcomed the remarks, although he pointed to Mr Bercow’s previous involvement with the hardline Tory Monday Club, notorious for its “hang Nelson Mandela” slogans.
At the age of 20, Mr Bercow left the pressure group, saying some of its members’ views about immigration were “unpalatable”.
Raising a point of order, Mr Blunt said: “I had hoped to raise this point of order directly with the Speaker as it arises from his exchange with [Ms Allin-Khan], who raised a point of order about racism in football.
“The Speaker gave us a homily on racism in football and its evils from the chair, which was particularly welcome coming as it does from a former secretary of the immigration sub-committee of the Monday Club.
“However, I have raised previously my concerns about the bias of the Speaker and I’d be grateful if you convey to him that the fewer views he expresses – either from the chair or as the Speaker – the less we will have anxiety about his bias.”
Deputy Speaker Sir Lindsay Hoyle replied: “I think we now need to press on with the business in hand.”