The federal parliamentary Speaker is under fire for using a charter helicopter to take an 100-kilometre journey from Melbourne to Geelong last year.
She's also facing criticism for spending $300,000 on travel in a year.
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Speaker Bishop to repay chopper costs
Mrs Bishop said in a statement on Thursday she had written to the Special Minister of State Michael Ronaldson indicating she would reimburse the costs associated with the November 5 trip.
"Whilst my understanding is that this travel was conducted within the rules, to avoid any doubt I will reimburse the full costs," she said.
Treasurer Joe Hockey had previously called for her to explain why she spent $5000 to fly to a Liberal party fundraiser, saying the claim on taxpayer money doesn't pass the "sniff test".
Asked if Ms Bishop's use of entitlements passed the sniff test, Mr Hockey said: "Instinctively, it doesn't".
"It is not a good look and the Speaker should explain it," he told radio 2UE on Thursday.
The Speaker's expenses include $130,889 spent on overseas travel in the later part of 2014.
An $88,000 16-day trip to Italy, Belgium, Austria and Switzerland came as she unsuccessfully campaigned to win the presidency of the Inter-Parliamentary Union, an international organisation headquartered in Geneva.
The Speaker's office has said her charter of the helicopter last November was done "in accordance with the guidelines and within entitlement" and that she made the journey "because of her concern for the country".
Mr Hockey said he understood the public anger over the affair.
However, the treasurer said it was a different matter to Peter Slipper, who faced calls to step down as Speaker by the coalition over his use of entitlements.
Mr Hockey said people were entitled to call for Ms Bishop's resignation.
But it was up to her to explain where the money went and how it was spent.
"I can only emphasise that the Speaker is the one that should explain the money," he said.
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