Commons Leader Andrea Leadsom said an independent inquiry into the bullying and harassment of clerks would be set up following explosive allegations by BBCNewsnight last week.
The Labour MP Paul Farrelly, another of those accused of bullying Commons staff in the Newsnight report last week, urged fellow MPs not to "jump to judgment".
Some shadow cabinet ministers have suggested that the counter-claims of bullying centre on Corbyn's chief of staff, Karie Murphy, which was strongly denied by the leader's office.
"Reports of bullying of house staff are of huge concern to me and to honourable members right across the house", Leadsom said.
Mrs Leadsom said the issue would be considered by the House of Commons commission at its next meeting and she would recommend the matter would be handled by an independent figure rather than MPs.
Insisting she was absolutely committed to "stamping out" all forms forms of bullying and harassment, she said it was not clear that the existing Respect policy setting out procedures for Commons staff not employed by MPs provided "sufficient" protection.
Having granted the urgent question to Ms Lucas as part of his job as speaker, Mr Bercow was present in the chamber for the session.
Bridgen, Conservative MP for North West Leicestershire, told James Whale that he and Bercow are not the best of friends.
Mr Bercow survived a backbench rebellion in 2015 - glowering at then Commons Leader William Hague when the results of a vote fell in his favour. Elected with the support of Labour MPs, Mr Bercow is disliked by many Conservatives, some of whom have complained that he has compromised his independence by speaking out against Brexit. "No one, critics or otherwise, can deny your commitment to accountability and transparency and attempts to move the house forward".
Mr Farrelly told the Commons that he had been "flayed by selective leaking" and said the Newsnight report had been "one-sided".
News that there is to be an investigation into Parliamentary bullying is likely to pile further pressure on Bercow, following allegations that his private secretary resigned in 2011 and suffered PTSD after working for him. "Given his apolitical position as Speaker of the House of Commons, he shouldn't be able to trumpet them from the rooftops as he does".
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