Federal MP Clive Palmer says he is calling on Speaker Bronwyn Bishop to resign because of her age and because she is "very biased".

Mrs Bishop has come under fire after it was revealed she used taxpayers' money to charter a helicopter to fly to a Liberal party fundraiser.

She is also facing questions about allowances she claimed around the weddings of Liberal colleagues Teresa Gambaro and Sophie Mirabella.

Mrs Bishop has apologised for "letting down" the Australian people, but said she would not resign.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 9 minutes 32 seconds 9 m Clive Palmer speaks on Lateline

Mr Palmer said Mrs Bishop had made too many mistakes to remain in the role, and Prime Minister Tony Abbott should act.

"She's demonstrated over a long period of time that she's very biased in the role of Speaker," he told the ABC's Lateline program.

"Bronwyn should know that if she resigns from Parliament she'll still get the same entitlements.

"She doesn't need to put us through torture for a year-and-a-half to get her own personal entitlement.

"She's been there a long time, over 20 years, and she's now 72 years of age. It's time to roll over and give a younger person a go I think."

Mr Palmer, a former life member of the Liberal Party, said half of the party thinks she should resign.

"Over half the Liberal Party think she should go as well but they're terrified to say so, to do something and to think," he said.

"I still talk to people, they haven't gone away, and they've all expressed concern to me."

Earlier this month, Mr Palmer and fellow MP Andrew Wilkie announced they would move a no-confidence motion in Mrs Bishop when Parliament resumes.

He said the Speaker should be chosen from one of the independent MPs and suggested Cathy McGowan.

"Why does it have to be a Liberal or a Labor speaker?" he said.

"I take it very seriously, being elected to Parliament to represent the people of my area. Why should I be denied a voice in Parliament because I've got a Labor or a Liberal Speaker?"

But Mr Palmer made it clear he had no aspirations for the job.

"I don't think I've got the ability or the temperament to be the Speaker," he said.

He said Mrs Bishop had breached the trust of the public and they had a right to be outraged.

"Can you imagine the headline 'Clive Palmer catches chopper at taxpayers expense'? I've got my own chopper," he quipped.

Finance department to investigate decade of Bishop's travel

The Federal Opposition said Mrs Bishop should be forced to show she had permission to travel to places her parliamentary committee was not holding public hearings.

The Guardian has reported Mrs Bishop claimed 15 trips in two years to places the Family and Human Services committee was not holding public hearings.

Sorry, this video has expired Bishop apologises for 'letting down Australians' with expenses scandal

The Speaker has asked the Department of Finance to look at her parliamentary travel to see if she has breached the guidelines, but it has so far refused to give details of which of Mrs Bishop's trips it is investigating.

Labor MP Pat Conroy said Mrs Bishop needed to show the public she was allowed to undertake that travel.

The department should also publicly release its report when it is complete, he added.

"I think it's up to Mrs Bishop to produce minutes or rulings that A: demonstrate that a committee chair can travel independently from their committee, and secondly, that those trips were authorised by that committee," he said.

"Given the fact the Minchin Protocol should not apply because I've referred the matter directly to the federal police, I think all these matters should be disclosed so the public do have confidence the Speaker's done the right thing and that they can have confidence in the Parliament."

The Prime Minister's office said the investigation will go as far back as a decade.