Ms Bishop, an ally of Prime Minister Tony Abbott, had used A$5,000 (Â£2,300) in public funds to charter a helicopter to attend a political fundraiser.
She also claimed expenses for attending colleagues' weddings. Mr Abbott said Ms Bishop's resignation was the right decision to take.
He announced that the parliamentary expenses system would now be reviewed.
"It won't just be tinkering with the system,'' he told reporters. "Plainly, the system that we have is deficient. The public deserves to be absolutely confident taxpayers' money is not being abused."
Mr Abbott has himself had to pay back money spent on travel in the past.
The helicopter flight in question was between Melbourne to Geelong - a journey of 65 km (40 miles).
Ms Bishop has apologised and is paying back the helicopter costs but had, until Sunday, resisted calls to resign.
"I have not taken this decision lightly," she said in a statement announcing her resignation.
"It is because of my love and respect for the institution of parliament and the Australian people that I have resigned as speaker," she added.
Australia's Department of Finance will review 10 years' worth of Mrs Bishop's travel claims and is due to report back "as soon as possible".
However, it is not clear if that report will be released to the public.
There are few things that put the public's back up more than a political expenses scandal.
There are few things that get journalists more excited.
This proved a lethal combination for Bronwyn Bishop's political future.
In light of Tony Abbott's conservative government telling people the "age of entitlement is over," it just didn't sit well for an MP to use A$5,000 of taxpayers' money to charter a helicopter to make a journey she could have driven in just an hour.
Especially when the taxpayer already forks out for Mrs Bishop to have a car and a driver for some of her travel.
Despite initially only receiving a slap on the wrist from the prime minister who put her on "probation", it became apparent over the weekend that Ms Bishop's refusal to resign from the Speaker's chair risked jeopardizing Mr Abbott's own political future.
The speaker of the lower house of the Australian parliament, Bronwyn Bishop, has resigned over an expenses scandal.