He said he apologised to Bungard, who is the Howick Local Board deputy chairwoman, during mediation that was facilitated by National Party president Peter Goodfellow.
But he accused the party of burying the matter by getting Ross and Bungard to sign non-disclosure agreements.
This morning Tau Henare, a National MP from 2005 to 2014, said via Twitter that heads should roll.
"More Heads should roll in @NZNationalParty over the #JLR meltdown. You cannot protect the abuser and hush the victim because it will hurt your brand. You damage your brand by covering shit up."
In another tweet, Henare said that the party hierarchy had handled Ross poorly by "sweeping shit under the mat. So much so that the story broke it victimised the women in question again. #HeadsWillRoll"
Henare told The Hui: "They are reaping all of what comes from a pretty poor decision and ... the president of the party, his head should be rolling down Willis St right now."
The party should have kicked Ross out when allegations emerged, he said.
"They should have walked into his office and said 'you're out, you're gone mate' ... they should have jumped on it hard and fast."
But Bungard said she didn't blame the party.
"I do want to make it very clear that I have always felt fully supported by the National Party and its leadership."
She said party president Peter Goodfellow acted as a mediator, and she and Ross signed an agreement to move on from their fallout in 2016.
"There was absolutely no exchange of money, or any documents signed that would suggest any kind of compensation. The party was simply doing their best to facilitate a meeting to bring an end to a situation which I had brought to their attention that was troubling me."
In a statement, Goodfellow has said of the matter: "Any issues that we were aware of that were raised were dealt with at the time. We have nothing further to add at this time."
Ross also accused the National Party of facilitating the media reports about the women, but this has been rejected by Newsroom and the party.
"The issues raised by the women who came forward are real and being taken seriously. They made their own decisions to come forward," a party spokesman said.
Ross has launched an extraordinary attack on the party and leader Simon Bridges over the past week, and has laid a police complaint over what he says is electoral fraud.
Bridges and the party have called Ross a liar and welcomed the police probe, saying they have done nothing wrong.
Ross was going to quit the party and force a byelection in Botany, but has now vowed to stay in Parliament and dish the dirt from under the political bedsheets, having had his own affairs exposed.
He has apologised to his wife Lucy Schwaner.
Bridges has said that he first heard about allegations of Ross' misconduct a few weeks ago.
"This is about supporting our colleagues at this time and the victims of this," Bridges said yesterday while at the Auckland Diwali Festival.
"We've made sure we've done that in recent weeks as we've learnt about this."
The party is considering its options, including the possibility of using the waka-jumping law to remove Ross from Parliament - a law that the party has been highly critical of.
