A day prior, Ross stood in front of press for an hour and launched a scathing attack on Bridges – calling him a "corrupt politician."
Bridges denied this and said the tape Ross released on Twitter showed no evidence of his claims.
"He is a liar, and he has defamed me."
Speaking to media before Question Time, Peters said Kiwis' would have been "shocked" to hear the way Bridges talked about Pugh.
"He seeks to make an apology which cannot possibly stand up against the flippant way he dismissed her and others."
Bridges also suggested, in the tape, senior MPs Chris Finlayson and David Carter were on their way out.
"I always knew that Finlayson – the greatest legal mind the Commonwealth has ever seen – was going and Mr Carter had gone by his used by date a long time ago."
Peters said Bridges is a "dead man walking, politically".
"I wouldn't put a timeline on it because stupidity has no bounds when it comes to political awareness but go he will, as leader".
NZ First MP Shane Jones said the "fiction" of the National Party had been laid bare.
"The National Party is a powerful party of white men. They are at the upper citadel of the economic pyramid and anyone who doubts that is dreaming."
The tapes also revealed Bridges talking bluntly the prospect of National having more Indian and Chinese MPs.
"Two Chinese would be nice but then, you know, would it be one Chinese and one Filipino? Or, you know, what do we do?" Bridges said.
Jones said it is important to reflect diversity, "but I've always felt that the National Party treated diverse ethnic groups, obviously not the Māori, as ATM machines.
"They are the political extension of powerful white men."
Jones said it was unlike anything ever seen and sent a "terrible" signal to young voters, the families of politicians.
"The scab's been ripped off ... the sooner we go through that episode the better. But this does lay open the truth. It's a powerful, political economic machine, it always has been."
