National MPs Nick Smith then accused Mallard of "bullying" behaviour on several occasions.
Out of the 56 National MPs, there were at one stage fewer than six left in the House, however a few began to return later.
Tensions have been building between National and Mallard over an alleged bias by Mallard against National and yesterday he accused Bridges of being "smart-arse" in his questions.
Mallard withdrew and apologised fairly soon afterwards.
One MP said that Bridges had not been thrown out because he accused Ardern of "ducking and diving" but because when the Speaker stood up to possibly reprimand him for the comment, Bridges said "here comes the protection".
When Question Time finished at 2.55pm, former Speaker David Carter took a point of order to ask the Speaker to look at his decisions this week in not pulling up ministers for attacking National during answers to questions.
He also asked Mallard to stop his practice of taking supplementary questions off National as punishment for what he sees are transgressions against the House's rules.
Mallard said he had thrown out Bridges for questioning his partiality.
He said would be looking over today's Question Time and will be "reflecting" on Bridges' comments.
He added that he had at times reverted to the practice that former Speaker David Clark used to use, by kicking Bridges and Brownlee out of the House instead of deducting supplementary questions.
"I'm still not convinced that on all occasions it is the right thing to do, but I do want to assure members that I will attempt to keep order in the House and part of that is making sure questions and answers are as far as possible, within standing orders and Speaker's rulings."
Speaking to media this afternoon, Bridges said he was kicked out of the House after claiming that Mallard was protecting Ardern from his questions about Sroubek.
He asked a question, and then said, "here comes the protection".
"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," Bridges said.
"Here we are talking about a victim [Sroubek's estranged wife], we're talking about very serious matters that there should be answers to, and that she knows about and she should know about as Prime Minister."
He said Mallard often leapt to his feet in the House over "pretty trivial matters".
He said other National MPs followed him out of the chamber because "they weren't happy with what they saw", and Brownlee was kicked out for trying to raise a point of order.
"My members do support me and they would have been very disappointed in what they saw happening there ... a Speaker who has shown himself to be protecting, rather than enabling an Opposition to get to the bottom of what's gone on."
Speaking to media outside the House, Deputy Prime Minister Winston Peters said what was most damaging about the walkout was the way other National MPs walked out after Bridges.
"They went out in dribs and drabs. It looked like the first loyal group of about six went out, then about 12 others decided they might be loyal, then the rest decided they better show some loyalty as well – it was seriously disorganised."
But a spokesman for Bridges said those who stayed in the House were MPs who had questions.
One such MP was Nikki Kaye, who said she stood by Bridges and other National MPs' decision to walk out.
National Deputy Leader Paula Bennett said it was "absolutely ridiculous" that Bridges was thrown out of the House.
Asked if she thought the Speaker was being biased against National, she said: "I'm not going to say that publically – there are rules around this place."
Immigration Minister Iain Lees-Galloway said it looked like the Opposition "wanted an early holiday – they couldn't handle the heat".
He called out Bridges for questioning the impartially of the Speaker.
Labour backbencher Greg O'Connor said the saga was "beautiful irony".
"It's so ironic that National, who spent all day yesterday opposing anything that resembled industrial action, today stage the most basic piece of industrial action, a walkout – I love irony."
