A separate, independent review into Labour's processes in dealing with the complaints would be based on evidence that had already been gathered by the party's lawyers Kensington Swan.
But Bridges questioned whether the independent review would include what Ministers and Beehive staff knew, including Ardern's advisers and Robertson.
"I think we need to know these things in order to have accountability on this.
"She [Ardern] set the terms of reference with others and they don't include him [Robertson], and they won't – and so he will not have to answer questions unless those terms of reference are changed.
"That's a whitewash."
Robertson this morning doubled down on comments he had previously made, saying the first time he knew about the detailed allegations of sexual impropriety directly from a complainant was in The Spinoff story last Monday.
"Beyond that, I don't think it's helpful to get into what I did or didn't know."
Asked again if he was made aware of specific sexual assault allegations, he said he did "not want to get into that".
He said he was "more than happy" to submit his experience to the inquiry if that's what is asked of him.
But he said he had acted "appropriately throughout this".
Bridges has also criticised some of Ardern's ministers in their handling of the situation.
"She said … that this is going to be victims at the centre; that it was all about that.
"And yet what is quite clear is her Deputy Prime Minister [Winston Peters] and the Deputy Leader of her Party [Kelvin Davis] are saying things that are very different."
Yesterday, Peters said the assault allegation saga was a "disgraceful orgy of speculation and innuendo".
"None of which I can tell you, even from where I sit and what I know, will be proven by the evidence," he told Newstalk ZB.
"What I saw unfolding is actually a disgrace."
Bridges said these types of comments were not conducive to the victim-centred approach Ardern said she was pursuing.
Asked about Peters' comments, Ardern said that was something she "was not going to engage in".
"The Deputy Prime Minister, obviously, is able to speak for himself."