As Opposition Leader Bill Shorten demands Tony Abbott ask Speaker Bronwyn Bishop to stand aside amid an investigation into her taxpayer-funded travel, the Speaker has labelled the allegations she misused her travel allowance a “political beat-up”.

Late on Sunday, Ms Bishop was still refusing to apologise for her “error of judgment” in charging taxpayers more than $5000 for a chartered helicopter from Melbourne to Geelong last year to attend a Liberal party fundraiser.

Her defiance came just hours before a Herald Sun report claimed that the Speaker took a second chopper flight in regional NSW just five days after her trip to Geelong.

According to the newspaper, Ms Bishop took the charter service to the NSW town of Young, where she was key speaker at the $50-a-head Liberal event at the Young Services Club.

The paper also wrote that the flight was not listed in the six-month audit of travel expenses by federal politicians.

• Surfer Fanning’s incredible shark attack escape
• Joe Hockey hitches a free ride on Air Bishop
• The solar giant stalking the PM
• Mystery surrounds Maccas sign in desert

Ms Bishop last week charged taxpayers $5227 for the return trip from Melbourne to Geelong. She 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.

Earlier on Sunday, 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.

Labor has called for Ms Bishop’s travel entitlement misuse claims to be handled the same way those against her predecessor Peter Slipper were.

“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,” Mr Shorten said.

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.

Standing her ground

Despite calls from Labor for the Speaker to step aside, Ms Bishop says the issue is regrettable because it has taken the pressure off the Opposition Leader.

Bronwyn Bishop and Bill Shorten exchange pleasantries in parliament. Photo: AAP

“There’s been a political beat-up and I’m very sorry it’s taken the heat off Mr Shorten and his triple-whammy carbon tax bill,” she said.

But Ms Bishop conceded the trip, from Melbourne to Clifton Springs Golf Club and back last November, was expensive.

“When I saw the figure, it looked large and I thought I should pay it, and am paying it,” she said.

Prime Minister Tony Abbott has thrown his support behind Ms Bishop, saying he will not be asking the Speaker to step down during the investigation.

At a Sydney press conference, Ms Bishop also said she would not be resigning as Speaker.

AFP investigation

In a letter to the AFP on Saturday, Labor’s waste watch spokesman Pat Conroy says refusing to investigate the allegations would be “inconsistent” with the AFP’s approach to allegations against former speaker Mr Slipper in 2012.

“I ask that your investigation into Ms Bishop’s conduct proceed without any further delay,” he wrote in the letter obtained by AAP.

The AFP declined Mr Conroy’s request for an investigation on Friday.

An AFP spokeswoman said the matter would instead be investigated by the Finance Department under the Minchin protocol, “the agreed protocol for dealing with matters of this nature”.

That’s despite the AFP having investigated Mr Slipper in 2012 over allegations he misused taxi dockets.

At the time, a Finance Department spokesman said the Minchin protocol did not apply where an allegation was referred directly to the AFP.

Mr Conroy said the Minchin protocol was “no impediment” to a police investigation into Ms Bishop’s conduct and was merely an administrative policy.

“This simple administrative policy cannot override the statutory obligation to investigate and prosecute crime which is imposed on the Australian Federal Police,” the letter says.

Labor wants the AFP to investigate whether Ms Bishop made a false statement when she signed a Finance Department form stating the charter was claimed for “official business”.

– with AAP, ABC