Australian Foreign Minister resigns
Bishop 62 said she had not yet decided whether to stand at the next general election due in 2019 reports the BBC.
She had sought the Prime Minister s post after Malcolm Turnbull stood aside but was eliminated in the first round.
The leadership fight also ended her 11-year tenure as deputy leader of the ruling Liberal Party.
"I will remain on the backbench as a strong voice for Western Australia " Bishop who has been a federal politician for two decades told the media.
Last week s leadership crisis arose after Turnbull came under pressure from poor polling and what he described as an "insurgency" by conservative MPs.
The Liberal-National coalition government has only a one-seat majority in parliament and Labor is ahead in opinion polls with a general election to be held at some point before May 2019.
--IANS ksk