David Leakey, a former Black Rod, and Angus Sinclair, an ex-private secretary, have accused senior figures of dragging their feet over complaints against Mr Bercow, who will step down from his role on Thursday.
Their intervention follows an announcement last week that parliamentary authorities were opening the Independent Complaints and Grievance Scheme to former staff and would consider allegations from before 2017.
But Mr Leakey, who served in the House of Lords from 2011 to 2017, told The Sunday Telegraph he expects the speaker to avoid investigation. He said Mr Bercow had been “aided by the supine approach to dealing with misconduct and poor behaviour by the leadership of all political parties.”
The report did not refer to allegations of bullying against Mr Bercow, which he has denied.
Mr Sinclair, who broke a non-disclosure agreement to report alleged bullying by Mr Bercow in 2018, told the Telegraph “the horse has long bolted” for investigating the speaker’s behaviour.
The former private secretary has accused Mr Bercow of mimicking him and said he was prone to “over-the-top anger”.
The alleged failure to act on misconduct has meant parliament “is not a safe place”, according to Mr Sinclair. He added: “The last year has shown me that when it feels it’s got more important things to do, that sort of thing doesn’t matter."
Dame Margaret Beckett, a long-serving Labour MP, caused outrage last year when she suggested Mr Bercow should not stand down over the handling of bullying and harassment because his work on Brexit “trumps bad behaviour”.
Mr Leakey said he doubts he will make a complaint via the new system, as there will not be time to investigate the outgoing speaker before he steps down.
“Bercow will soon be outside the jurisdiction of parliament and there would be no sanctions that could be applied against him by the time a complaints process was complete, if it found him to have behaved inappropriately,” he said.
In 2018, Mr Leakey described an incident in which Mr Bercow allegedly “banged the table, yelled and was highly insulting to me personally” after the “red mist descended” on him.
He added the former Conservative MP should be denied the peerage that is usually given to former Commons speakers.
If Mr Bercow was awarded a peerage "it would be a scandal parliament would struggle to live down,” Mr Leakey said.
A spokesperson for Mr Bercow has insisted there was “no substance” to the allegations by either man.
The new speaker is due to be elected by MPs on 4 November, with Mr Bercow’s three deputies and former Labour deputy leader Harriet Harman running as candidates.
Additional reporting by PA