The Federal Opposition has ramped up pressure on Speaker Bronwyn Bishop, asking the Australian Federal Police to investigate whether she has misused her parliamentary travel entitlements.

Mrs Bishop has agreed to repay $5,227 of taxpayer's money she spent chartering a helicopter from Melbourne to a Liberal Party fundraiser in Geelong in November last year.

The Speaker said while it was her understanding that the travel was conducted within the rules, she was repaying the money, with a 25 per cent loading on top, to "avoid any doubt".

The Opposition has questioned that explanation and has written to the AFP asking it to investigate the matter.

Opposition finance spokesman Tony Burke said Mrs Bishop has refused to produce a copy of the form she signed confirming that the trip to Geelong was for official business.

"This is a disaster, what Bronwyn Bishop is currently doing, and for somebody who has already gained a reputation as one of the worst Speakers ever, we're in a situation now where she will not answer a basic question — which is, has she or has she not lied on a form which if you lie on carries criminal penalties?" he said.

"Now, there are times when people make honest mistakes.

"There are times when an administrative error is made, where someone makes an honest mistake.

"But for the life of me, I don't see how someone accidentally gets on a helicopter and ends up at a Liberal Party fundraiser."

Mr Burke said Mrs Bishop had "gone to ground" since the story broke this week and has refused to properly explain the reasons for her travel.

"For that reason, the Chair of our Waste Watch Committee, Pat Conroy, has written today to the Australian Federal Police asking for them to investigate what Bronwyn Bishop is currently trying to hide," he said yesterday.

"If there is a reasonable explanation, then Bronwyn Bishop should give it to the Australian people, and she should provide it to the Australian Federal Police."

As Manager of Opposition Business, Mr Burke frequently clashes with Mrs Bishop, accusing her of bias in her role as Speaker.

Parliamentary records show Opposition MPs have been booted from the House of Representatives Chamber 394 times, compared with just eight members of the Government.

Independent senator Nick Xenophon has long been calling for an overhaul of the travel entitlements system and is hoping this latest controversy prompts the Government to act.

"I think Bronwyn Bishop finally realised she miserably failed the pub test when it came to this expense," he said.

"Bronwyn Bishop may have complied with the rules but I think the rules need to be overhauled to be more transparent."

Senator Xenophon said MPs should be forced to fly economy and all travel should be declared every 30 days, rather than every six months.