Federal Labor has again called into question Bronwyn Bishop’s impartiality after allegations the Speaker used her parliamentary suite for fundraising purposes.

Bishop reportedly hosted a Liberal party fundraising event in her suite on the night of the 13 May budget. Labor says if the claim is proven, Bishop should stand down.

“If this is true, her position as Speaker is no longer tenable,” the manager of opposition business, Tony Burke, said.

He said the Speaker’s office was meant to be owned by the parliament: “It’s not a venue for hire.”

A spokesman for Bishop said she had not broken any electoral laws by holding the fundraising dinner. No taxpayers’ funds were used and all costs associated with Bishop’s private functions were charged to her private account.

“The Speaker does from time to time have private functions at parliament, as do many other members and senators,” the spokesman told News Corp.

Labor has previously questioned Bishop’s “serious partiality” in her rulings and it unsuccessfully moved a motion of no confidence in her in March.

On that occasion, Labor had attempted the first vote of no confidence in a parliamentary speaker since 1949, declaring Bishop biased, incompetent and failing in her interpretation of the standing orders.

Labor brought the vote on after the shadow attorney general, Mark Dreyfus, was “named” when he called out “Madam Speaker”. Being named requires him to leave the chamber for 24 hours, rather than the usual one hour under the standing orders.

The Labor motion charged the Speaker with serious partiality in favour of the government; a failure to interpret the standing orders, and gross incompetency in parliamentary procedure.

“[The Speaker] regards herself as an instrument of the Liberal party and not as the custodian of the rights and privileges of elected members,” Burke said in moving the debate, adding that 98 Labor members had been thrown out of the chamber since the 44th parliament began.

The opposition lost, by 83 to 51, the vote on a suspension of standing orders to bring on the no-confidence vote. The independents Andrew Wilkie and Cathy McGowan voted with the government; Adam Bandt, of the Greens, voted with Labor. Clive Palmer and Bob Katter were not in the chamber for the vote.

The leader of the house and education minister, Christopher Pyne, who managed opposition business for five years, led the government attack on the motion and called Burke a “great big sook”.

The day before, Bishop had chided the Labor member for Franklin, Julie Collins, for laughing.

“We seem to have a new tactic of having an outburst of infectious laughter, which I suspect may become disorderly, and I suspect it might begin with the member for Franklin. The member for Franklin is warned,” the Speaker said.

“Are you ruling people out of order because they are laughing?” Bishop was asked.

Collins was ejected, as were fellow Labor members Terri Butler, Pat Conroy, Mark Dreyfus, Chris Bowen, Brendan O'Connor, Matt Thistlethwaite and Nick Champion.

More recently Bishop was again under fire when social media erupted after a video circulated showing Pyne directing her to stand up in order to cut off applause for the leader of the opposition, Bill Shorten, after his budget-in-reply speech. Bishop immediately rose from her seat.