Bishop, a member of Abbott's Liberal Party, had been under fire for more than three weeks as media reports emerged of her use of taxpayers' money for trips including spending AUD 5,000 (USD3,600) on a 80-kilometre helicopter ride for a November political fundraiser.
"I have not taken this decision lightly, however it is because of my love and respect for the institution of parliament and the Australian people that I have resigned as Speaker," 72-year-old Bishop, who has served in the role since 2013, said in a statement.
"What has become apparent, particularly over the last few days, is that the problem is not any particular individual, the problem is the entitlements system more generally," the conservative leader told a press conference.
"There are still too many situations where members of parliament can do things which are inside entitlement but outside public expectations."
Abbott declined to criticise Bishop -- a veteran Liberal who has been described as his political mentor -- but said her resignation tendered to the Governor-General was the "right thing by the parliament, by the government and by the people of Australia".
Her travel claims are being reviewed by the government's finance department.
