The Speaker's office has refused to comment on reports Bronwyn Bishop spent $6,000 chartering a plane for a 160-kilometre trip from Sydney to Nowra last year.

Mrs Bishop was invited to speak at two seniors' forums in the marginal electorate of Gilmore in November and, while she was there, attended two fundraisers for local Liberal MP Ann Sudmalis.

News Corp has reported the private plane cost taxpayers $6,000 but a spokesman for Mrs Bishop would not confirm or deny the report.

"These matters are now being reviewed by the Department of Finance and it would be inappropriate to continue commentary now this process is underway," the statement said.

Labor frontbencher Tony Burke has seized on the report which suggests there is a personal link between Mrs Bishop's office and the charter company she has been using.

"These allegations take this entire saga to a new level, to an absolutely new level," he said.

"What we're talking about now is not simply whether the rules have been broken but whether or not there's an extra layer of completely inappropriate conduct."

Mrs Bishop has been under sustained pressure after it was revealed she spent more than $5,000 chartering a helicopter from Melbourne to Geelong in November to attend a Liberal Party fundraiser.

The Speaker repaid the money, with a 25 per cent penalty, and last week apologised to the Australian public for what she described as a "ridiculous" claim.

But that has not satisfied Mrs Bishop's critics, with the Opposition calling on her to resign as Speaker, and independent MP Andrew Wilkie and Palmer United Party leader Clive Palmer announcing they would move a motion of no-confidence in her when Parliament resumes on August 10.

Mr Wilkie said Mrs Bishop was "undoubtedly a serial abuser" of parliamentary entitlements and was "entirely unfit" to be the Speaker of the House of Representatives.

"She must step down immediately from the position and repay every cent," he said.

Foreign Minister and deputy Liberal leader Julie Bishop said there were "grey areas" in the entitlements system, but MPs ultimately need to use their judgement.

"I don't want to go into a running commentary on each and every expense claim of each and every member of parliament because I understand the Department of Finance is looking into Speaker Bronwyn Bishop's claims," she told Channel 9.

"There are many grey areas in parliamentarians' entitlements between party functions, between community functions.

"It comes down to judgement."