Bridges said he had predicted Peters' reign as acting PM would be a "snoozefest" but was rapidly revising his opinion.
"We are about to have Acting Prime Minister Winston Peters and his very first act is to sue his own government and to sue the most senior civil servant in the land, Peter Hughes.
"I think he should focus on government and New Zealand, not his own personal vendetta."
Ardern told Newstalk ZB the legal action was a personal decision by Peters and she had not discussed in any great detail with him.
She said it was not her place to try to direct him on the matter or persuade him one way or another.
"It has not affected his ability to do the job to date. It is one extra step in a case that is a private matter for him and a decision for him. It's not something I'm involved in and nor should I be."
She said Peters would not take part in any Cabinet discussions on the case, including whether the legal costs of the former ministers will be paid for by the Crown.
Cabinet had agreed to cover the legal costs of the former ministers involved in earlier proceedings by Peters and will have to consider whether the costs will be covered for the fresh action.
The Cabinet Manual provides for former ministers' legal costs to be covered in cases where they are sued for actions in their roles as ministers if Cabinet approves it.
Cabinet Directions also provide for the Crown to cover the legal expenses of civil servants who are sued in the course of their duties.
That will be based on advice from Attorney General David Parker and Ardern said she had "absolute confidence" it would be handed properly.
Bridges said he had not spoken to Bennett and Tolley about it since becoming leader, but had informally spoken to those involved in the past. He said they were adamant they had not leaked it.
Bennett and Tolley were both briefed about the overpayments by Hughes and Boyle under the "no surprises" policy operating between ministers and the public service but have denied leaking the information to media.