LABOR is again calling on police to investigate Bronwyn Bishop, claiming the Speaker’s growing catalogue of misused expenses justifies an inquiry.

Opposition waste watch spokesman Pat Conroy wrote to the Australian Federal Police on Saturday to ask that the agency reconsiders its decision not to check whether Mrs Bishop committed a serious offence over her use of travel entitlements.

It comes amid fresh claims the embattled Speaker spent $6000 to hire a luxury corporate aircraft for a 160-kilometre journey from Sydney to Nowra late last year to attend a party fundraiser. The trip came just two weeks after Mrs Bishop’s infamous helicopter charter trip from Melbourne to a Liberal fundraiser in Geelong.

“I believe the growing catalogue of misuse and the possible commission of serious offences warrants a police investigation,” Mr Conroy wrote.

Labor is also demanding answers about Mrs Bishop’s links to the aviation company she used.

The charter company has links to her and her chief of staff, News Corp says.

Opposition Leader Bill Shorten renewed his calls for Mrs Bishop to stand aside, saying new claims took her alleged misconduct to the next level.

“If Mrs Bishop’s personal relationships influenced her decision to repeatedly hire a particular company, then that is incredibly serious,” he told AAP in a statement.

Independent MP Andrew Wilkie went further, accusing Mrs Bishop of fraud.

Mr Wilkie, who plans to move a no-confidence motion against the Speaker when the parliament resumes, also believes Mrs Bishop and her office’s “questionable business dealings” with aircraft charter companies should be investigated by the AFP.

She had been certifying as official travel trips what most people would consider private, he said.

“In my opinion, this is fraud and should be dealt with as a possible criminal matter,” Mr Wilkie said.

Mrs Bishop has apologised amid the furore over her expenses, but refuses to step down as Speaker.

Labor will support a no-confidence motion against Mrs Bishop, but with the government having the numbers in the House of Representatives, the move is expected to fail.

The government says the Finance Department investigation should be allowed to run its course.

But deputy Liberal leader Julie Bishop admitted the government was having difficulty getting traction on other issues.

“It can be difficult if your surname is Bishop,” Ms Bishop said. The Speaker’s chief of staff, Damien Jones, could not be reached for comment today.