Speaker Bronwyn Bishop has apologised for "letting down" the Australian people but says she will not resign amid increasing pressure over her use of taxpayer-funded travel entitlements.

Mrs Bishop has been under scrutiny for more than two weeks after it emerged she used taxpayers' money to charter a helicopter to fly in to a party fundraiser.

While continuing to maintain the spending was within her entitlements, the Speaker fronted the media at an event in regional Victoria to say sorry.

"I am so apologetic to the Australian people for letting them down and I will be working very hard to make sure things are right," she said.

The angst was triggered by the revelations of Mrs Bishop's helicopter flight from Melbourne to Geelong.

She then faced further questions about allowances she claimed around the weddings of Liberal colleagues Teresa Gambaro and Sophie Mirabella.

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The veteran MP said she wished she had delivered the apology sooner and conceded the damage the expenses saga had done to her relationship with voters.

"It's important for me to talk with the Australian people," she said.

"I love this country very much and it does sadden me that I feel I've let them down."

Mrs Bishop has repaid the money for the charter flight and said she would also refund taxpayers for the expenses claims around the weddings.

Opposition Leader Bill Shorten described it as a hollow apology made for selfish reasons.

"If Bronwyn Bishop was genuinely sorry, she would not have waited nearly three weeks to say so," Mr Shorten said.

"There's a difference between saying sorry because you mean it and saying sorry because you're about to get the sack."

Mrs Bishop was asked about Labor's criticism, to which she responded: "This is a genuine apology."

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Privately, a number of senior members of the Government have questioned whether Mrs Bishop can remain as Speaker when Parliament returns in less than a fortnight, with one describing her position as "untenable".

But she said she would not relinquish the speakership.

It has been 15 days since media reports began to emerge about the helicopter flight and Mrs Bishop said she now conceded the decision to charge taxpayers for the charter was "unacceptable" and "inexcusable".

"The helicopter was just ridiculous," she said.

"It was too much money. It just looked wrong. Although it's within the rules, it just doesn't look right and therefore I am apologising and repaying."

She said Prime Minister Tony Abbott did not direct her to make the apology or repay the money.

Speaker wants further review of her spending

Mrs Bishop said she had asked Mr Abbott to direct the finance department to review her broader entitlements spending.

The department is already investigating a referral from Labor into the helicopter trip.

Mrs Bishop said she was personally trawling back over her records to check claims for other weddings and wanted the department to independently consider her spending.

Cabinet minister Peter Dutton said both sides of politics have had to make repayments in the past.

"If people breach the rules, even inadvertently, there's a penalty you pay, you repay the money," he told Macquarie Radio.

"But there are no crooks in politics in my judgment."

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Another Government frontbencher, Kelly O'Dwyer, described Mrs Bishop's apology as "heartfelt" but stopped short of providing the Speaker with her support.

"I'm not going to prejudge the process. It's ongoing at the moment and I think it's right that it be concluded," she told Sky News.

Ms O'Dwyer said it was important the Department of Finance inquiry was publicly released.

"It's right and proper that it be made public. There can be no ... opaqueness when it comes to the use of taxpayer dollars."

Treasurer Joe Hockey was also questioned about whether the Speaker's actions were harming the Government.

"There are many, many issues that are more important for Australia at this point in time, and I'm focusing on those important issues," he said.

"I'll leave the Speaker to explain issues for herself, as she has. I have nothing further to add."

'People will keep digging', former speaker says

Former Labor speaker Anna Burke said the intense scrutiny on Mrs Bishop would continue and that she should resign.

"People will keep digging, what other claims are going to turn up?" the Victorian MP told ABC News Breakfast.

"At what point does someone say, 'actually, we are bringing the whole institution — all of us — are being brought down by this'. Something needs to give."

Mrs Bishop has acknowledged there needs to be closer consideration of the way politicians spend public money.

"The rules should be looked at because there are lots of grey areas," she said.

"I think it would be helpful to have certainty."

Crossbench MPs Clive Palmer and Andrew Wilkie are planning to move a no-confidence motion in Mrs Bishop when Parliament resumes.

Mr Palmer has suggested Cathy McGowan, the independent member for Indi, would be his pick for a new speaker.

"We need a speaker that's independent and one that's beyond controversy because it's an important job to do for Australia," he said.

The maverick Queensland-based MP meanwhile has posted a bizarre video on his Facebook page bidding farewell to Mrs Bishop.

Mr Palmer repeatedly says "Goodbye Bronwyn" during the 11-second clip before signing off "Twittle-too".

Timeline of Bishop's travel scandals Claims $600 for return flight to Albury - June 9, 2006 Mrs Bishop flies into Albury and then continues on to Wangaratta for the wedding of former Liberal frontbencher Sophie Mirabella. Her office says the travel was within her entitlements because Mrs Bishop held a private meeting in relation to her role as chair of the family and human services committee in Albury and paid for her own transport and accommodation for the wedding. Claims $288 for travel allowance in Brisbane - 15 April, 2007 On the same day, Mrs Bishop attends the wedding of Liberal colleague Teresa Gambaro. Her office says the travel was within her entitlements because she was chair of a parliamentary committee looking into illicit drug use, and met with an academic with experience in that area the next day in Brisbane. Claims $5,227 for charter helicopter to Clifton Golf Course near Geelong - November 5, 2014 Mrs Bishop takes the 90km trip from Melbourne to the golf course for a Liberal fundraiser. The charter claim is recorded in the entitlement log and revealed as a helicopter flight when a tweet from a volunteer at the golf course surfaces. Helicopter claims emerge - July 15, 2015 Media starts reporting on the charter helicopter flight. The Speaker holds a media conference to defend her actions. She says the claim was within her entitlement but agrees to pay back the money with a 25 per cent penalty because of the public uproar. Flight referred to the AFP - July 17, 2015 Labor refers the helicopter flight to Federal Police for further investigation. AFP responds by invoking the 1998 "Minchin Protocol" and hands the case to the Department of Finance to investigate. No confidence motion announced - July 29, 2015 Crossbenchers Clive Palmer and Andrew Wilkie signal plans for a no-confidence motion when Parliament resumes. Bishop apologises - July 30, 2015 Mrs Bishop goes on Sydney radio station 2GB to say she is sorry to have "let down the Australian people" and vows to repay any taxpayer money she spent on attending weddings. However, she says she will not resign as Speaker.