Nine MPs are battling to be the next Commons Speaker ahead of an election in November. Mr Bercow, who has sparked controversy over his Brexit interventions and faced allegations of bullying, is standing down on October 31.
Speaking at today’s hustings event, Tory MP Shailesh Vara, who is vying for the role, hit out at Mr Bercow.
Mr Vara insisted he had "tarnished the role of Speaker with his bias”.
He added the rulebook needs to be rewritten to “make it absolutely clear what the Speaker can and cannot do in difficult circumstances”.
John Bercow has been accused of being a “verbal playground bully”
The Tory MP said: “Recently we have had a lot of debate about the standards of MPs in the Commons, and given that the Speaker Bercow has at times behaved like verbal playground bully in the way that he treats his colleagues.
“He insults them, he demeans them, I think that he loses all authority to lecture MPs as to how they should behave when his own behaviour is in question.”
Mr Vara added: “So I think that the Speaker should always be courteous and polite, authoritative yes, but not demeaning to his colleagues.”
Candidates lining up to replace Mr Bercow were questioned for around two hours by journalists.
The other MPs in the running are Sir Henry Bellingham, Chris Bryant, Harriet Harman, Meg Hillier, Sir Lindsay Hoyle, Dame Eleanor Laing, Sir Edward Leigh and Dame Rosie Winterton.
The election for the next Commons Speaker will take place on November 4, after Mr Bercow - who has held the office since 2009 - takes the chair for the final time on October 31.
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During the hustings, Sir Edward said Mr Bercow was "perceived by a large part of the nation not to be impartial".
Ms Harman, who is Mother of the House, said the role of Speaker was about being the "champion of Parliament in our parliamentary democracy".
The former Labour deputy leader added: "When it comes to a decision when Parliament is challenged, or when Parliament wants to have its say, or Parliament wants to vote, the Speaker must be the servant of Parliament and not impartial or neutral on that."
Candidates were also asked about the chaotic scenes last month in Parliament ahead of Boris Johnson’s prorogation, which was later ruled to be unlawful by the Supreme Court.
Mr Bryant said he hated the “chaos in the chamber”.
He added: “I didn't think that did us any favours. I thought it was crazy that we were doing it at 2 o'clock in the morning or whatever it was.”
Ms Hillier said: "I think it was one of the most unedifying moments in our parliamentary history to have all that singing, shouting. It was very uncomfortable."
Mr Bercow announced last month that he would be standing down as Speaker while his wife Sally Bercow watched from the public gallery.