The Australian National University chancellor again rejected accusations of bullying and harassment and declared there were "no grounds" for her to step aside.
Embattled vice-chancellor Genevieve Bell announced her resignation on Thursday following major discontent over controversial plans to cut academics at the university in a bid to fill a $250 million shortfall.
Ms Bishop was grilled on Thursday over allegations levelled at her by academic Liz Allen, who told a parliamentary hearing earlier in 2025 she had been bullied almost to the point of suicide by the former foreign affairs minister.
Ms Bishop said she had the support of the university council and would serve out the remainder of her term, which ends in 2026.
"I reject the allegations that I heard for the first time on the 12th of August that I have treated any staff at ANU with anything other than the greatest respect and civility and courtesy," she said.
"There are no grounds for me to stand aside."
The former federal Liberal Party deputy leader said she had placed a right of reply with the parliamentary committee last Monday and was awaiting confirmation it will be made public.
"I will not further compromise the integrity of a workplace grievance process that has now been put in place by the council," Ms Bishop said.
"I recused myself from these discussions and that there will be an independent investigation into these allegations."
Staff attending a town hall at the university on Thursday cheered and clapped when they were told Professor Bell had resigned.
Rebekah Brown will serve as an interim replacement and has vowed to review the unpopular cost-cutting "Renew ANU" program.
Education Minister Jason Clare said "significant governance concerns at ANU" had been raised with him and he had referred them to the Tertiary Education Quality and Standards Agency for assessment.
The Friends of the ANU School of Music president, Professor Paul Dugdale, said cuts that would "destroy" the music school would still go ahead.
"Every college at ANU is still facing major cuts, and the cuts proposed to the School of Music are more severe than for any other school," he said.
ACT senator David Pocock said Ms Bishop's tenure remained a decision for the university's council.
"There are some real questions around the governance of the ANU," he told the the ABC.
"There should be ... the sort of gold standard of governance, and that's clearly not the case at the ANU."
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