"I will do everything within my power to keep the things we talked about last week out of the public [inaudible]. I will do everything."
Bennett told Ross that leave would be the best course of action, and if he didn't accept, the issue would go before caucus.
They also discuss Ross' treatment of women.
"You haven't even told me what I've supposedly done," Ross says.
Bennett replies: "Simon told you all about the disloyalty stuff Jami-Lee, and quite frankly if that was put to caucus, that would be enough."
It is unclear what the "disloyalty" is referring to, as the conversation was before Ross was fingered as the likely leaker of Bridges' travel expenses.
Ross rejects any suggestion of harassing staff: "That is the worst. I don't even know what that is," he says on the tape.
At one point, Ross apologises to Bridges for a heated exchange that took place when the allegations first surfaced.
Following the tape's release, Bridges denied that he was prioritising Ross or the party's reputation over of the complainants and their allegations.
"We were dealing with a very serious, complex matter and balancing and factoring in allegations of inappropriate and disruptive conduct with very serious health matters," he told Newstalk ZB.
"I know that we were acting in accordance with the women's interests and what they wanted, but I had to also balance a situation where the person concerned had very serious health issues, and we were getting specialist advice on how to do with that."
He said his actions were appropriate, given the circumstances.
"I did the right thing here. I was trying to act with immediacy whilst also being clear that we couldn't have Jami-Lee Ross in the workplace and he needed time to get well on leave."
In the tape, Bridges and Bennett state repeatedly that they are concerned about Ross' mental health - and tell him if he follows their instructions he could return to Parliament next year - and he might even return to the front bench.
Bennett suggests citing medical reasons for Ross taking leave as it would reduce interest form the media.
"So it would be for medical reasons?" Ross asks.
"Is that what you want?" Bennett replies.
"I think either medical or family."
"Medical is true," Ross says.
"That's right," Bridges says. "There's no shame in that."
Bennett: "And it means everyone will back off you too - the media and all that sort of stuff."
Ross subsequently went on leave for personal health reasons and was later identified by an inquiry as the chief suspect for leaking Bridges' travel expenses.
The Botany MP has been expelled from the National Party but plans to return to Parliament as an independent MP.
He remains on sick leave.