Opposition Leader Bill Shorten has demanded Prime Minister Tony Abbott ask Speaker Bronwyn Bishop to stand aside amid an investigation into her taxpayer-funded travel.

Mrs Bishop is still refusing to apologise for her "error of judgment" in charging taxpayers more than $5,000 for a charter flight from Melbourne to Geelong last year to attend a Liberal party fundraiser.

She has repeated her view that repaying the money with an additional penalty fee was an apology in itself, but said she acted within guidelines because she was attending the function to speak about the work of the Parliament.

The Finance Department is investigating whether Mrs Bishop improperly used taxpayer funds, but Labor believes it should be a matter considered by the Australian Federal Police (AFP).

Mr Shorten said the "arrogant misuse of taxpayer funds needs to be held to account".

"This has now become a test of Tony Abbott's leadership — does Mr Abbott have the character to tell Bronwyn Bishop to stand aside?" Mr Shorten told reporters in Melbourne.

But Mr Shorten said it was up to the AFP to decide whether it would handle the investigation.

"The sheer act of writing to the AFP to ask them to investigate matters which are of concern to the public, in and of itself, is an appropriate thing to do," he said later.

"We recognise that the AFP's independent, they'll make their own decisions about what they choose to investigate or not, and that's as it should be."

The Greens have also called for the AFP to handle the investigation.

Senator Lee Rhiannon said the matter should be handled in the same manner as the investigation into former speaker Peter Slipper's use of his parliamentary Cabcharge allowance to the value of $954.

"The Australian Federal Police need to reassess their decision," she said.

Sorry, this video has expired Speaker Bronwyn Bishop defends her response to claims she misused her travel entitlements

"They are now becoming politicised in this. Why did the Australian Federal Police investigate Peter Slipper for $900, but are now refusing to investigate the current Speaker Bronwyn Bishop for $5,000 of travel expenses?"

Treasurer Joe Hockey openly criticised Mrs Bishop when details of her helicopter flight emerged.

Mr Hockey was asked on The Bolt Report yesterday if Mrs Bishop was entitled to claim travel expenses at all to attend a Liberal fundraiser.

"My understanding is that you need to be doing your duties as a Member of Parliament," he said.

"Now, the Speaker has a privileged position.

"As Speaker of the Parliament, the entitlements that she has [a] need to comply with all the rules and guidelines. The Department of Finance is investigating it."

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The Treasurer was asked if he had claimed travel expenses to attend a fundraiser but he did not give a clear answer.

"Well, we all raise money for our political parties. We all have a duty to raise money as a Member for Parliament," he said.

"I haven't heard of anyone who has taken a helicopter to a fundraising event."

The ABC asked Mr Hockey's office to clarify if he ever claimed travel expenses to attend a party fundraiser.

The spokeswoman responded: "I have always complied with requirements."

Mr Shorten has been asked if he has used his travel allowance to go to a Labor Party fundraiser.

"I don't believe so and I certainly know that I haven't caught a helicopter to go to a fundraiser," he said.

Bishop spent $14,000 on private cars in two-week Europe trip

The comments came as more details emerged of Mrs Bishop's taxpayer-funded trip to Europe last year, including a $14,000 bill for private cars.

Mrs Bishop spent more than $88,000 on a 15-day official visit to Europe while she was running for the presidency of the Geneva-based Inter-Parliamentary Union.

The Speaker has defended the trip.

"All I say about the international travel is that it is exactly the same as former presiding officers have done," she said.

"The president of the Senate, who led the delegation to the same meeting 12 months before, spent $92,000 so it is simply the way delegations are arranged."