National MP Gerry Brownlee says it's concerning the Speaker has twice intervened in Parliament's question time when tough questions were being asked of the government.
Following a series of questions to the prime minister yesterday on convicted Czech drug smuggler Karel Sroubek, Mr Bridges said "here comes the protection," implying Speaker Trevor Mallard was jumping to Jacinda Ardern's defence.
Subsequently, Mr Bridges was kicked out.
"I was asking the prime minister serious questions about the Sroubek fiasco, she wouldn't answer and the Speaker leapt to protect her. I called him on it," Mr Bridges told reporters afterwards.
It was put to him Mr Mallard would view that as a serious challenge to his authority as Speaker.
The Shadow Leader of the House Gerry Brownlee was also told to leave for saying Mr Bridges comment had "struck a raw nerve".
Mr Brownlee told Morning Report the questions posed by the Opposition on the Sroubek case were legitimate and reasonable.
"It's, for us, somewhat perplexing that the [Karel Sroubek] story has shifted ... and no real answers coming through and no definitive positions being taken about 'where to from here'.
"I think in this case it looks too much like the Speaker is sensitive to the prime minister's difficulty in answering questions."
The interruption by the Speaker raised some concern considering a previous remark by the Speaker two days ago, Mr Brownlee said.
"I think for the Speaker to interrupt the questioning two days in a row, not just yesterday, the day before with quite a derogatory comment and colourful comment made about the leader of the Opposition, is a little bit concerning," he said.
However, he said he understood the Speaker's role and the difficulties it posed but added the comments seemed to be unprecedented.
"I think there's never been a Speaker who has attacked the leader of the Opposition with the sort of language we saw the other day."
After the heated question time yesterday and Mr Bridges leaving, the National caucus followed him out.
"I think it was more of an individual commentary from members that they wanted to support Simon Bridges and demonstrate to the Speaker that they didn't think the value that should come out of question time was available to the public," Mr Brownlee said.
Yesterday, Ms Ardern rejected any accusations she was not fronting questions on the matter, and Mr Mallard declined to comment on the criticisms levelled against him by Mr Bridges.
Mr Brownlee said it would be interesting to see what the atmosphere in Parliament was like today but did not expect any significant problems to arise as a result of yesterday.
"Sometimes what we consider to be heated moments in Parliament are not of the level that might cause significant problems [like in some] other countries."