The Australian Federal Police say an internal government investigation will be undertaken into an allegation House of Representatives Speaker Bronwyn Bishop misused her travel entitlements.

Labor yesterday wrote to the AFP asking it to investigate the Speaker's use of a chartered helicopter to attend a Victorian Liberal Party fundraiser last year.

Mrs Bishop said she believed the use was within travel rules but would repay the $5,227 cost to "avoid any doubt".

The AFP has said it would refer Labor's allegation to the Department of Finance which would conduct an internal investigation.

It could then ask for an explanation from Mrs Bishop or refer the matter back to the federal police.

Last November Mrs Bishop chartered a helicopter for a 90-kilometre trip from Melbourne to a party fundraiser near Geelong.

The cost of the trip was revealed in the Speaker's six-monthly report to the Finance Department.

Her Liberal colleagues conceded the trip did not pass the "sniff test" and called on Mrs Bishop to provide an explanation.

On Thursday Mrs Bishop released a short statement confirming she would pay for the flight herself.

"I have today written to the Special Minister of State indicating I will reimburse the Department of Finance the costs associated with the use of my charter allowance on 5 November 2014," the statement said.

"Whilst my understanding is that this travel was conducted within the rules, to avoid any doubt, I will reimburse the full costs."

The Speaker's office confirmed she would also pay an additional 25 per cent penalty under expenses rules announced by the Abbott Government in 2013.

The Opposition questioned Mrs Bishop's explanation and said she had refused to produce a copy of the form she signed confirming the trip to Geelong was for official business.

Finance Minister Mathias Cormann acknowledged the controversy was distracting from the Government's message.

Senator Cormann told Sky News that he could not say too much because the matter was now being investigated by the Finance Department.

"I would much rather be talking to you about our plan to strengthen growth, create more jobs and to repair the budget," he said.

"Of course I would much rather talk about the issues which are important to the Australian people."

Independent senator Nick Xenophon said he expected Mrs Bishop to retain her job.

"It's tenable while she has the support of the Prime Minister and since she's one of the Prime Minister's favourites, I think it's tenable for the time being," he told Sky News.