Of all the candidates, Joyce is the closest to the mould of the John Key and Bill English empire.
He is believed to have the support of senior MPs concerned about of the future of the party should Joyce leave, given his strong influence over the party's strategy and caucus management.
Bridges took apparent aim at that, saying there were some who believed National only had to keep doing what it was doing to get back in in 2020, when it needed to "freshen up".
The role of deputy leader will now also go to the vote next Tuesday. Whip Jami-Lee Ross said Bennett had suggested to him last week that it should be voted on and caucus had agreed.
No others have yet said they will contest it although it is possible the successful new leader could put up their preferred deputy or a deal struck with one of the unsuccessful candidates.
That could raise the prospect of the deputy being perceived as undermining the leader if the deputy's own leadership ambitions are known.
Bennett has pointed to her own lack of ambition for the leadership as one of her merits, saying she had been a "loyal" deputy and enjoyed the job.
Bennett did not believe having women as both leader and deputy would be a problem.
"Absolutely not. It's 2018. We've had two men plenty of times. I think getting that personality mix right, that skill mix right is far more important."
Joyce said he was focusing on the leadership rather than beyond and if he did not win, he would serve whoever did.
He said it would be a contest of ideas over the future direction of the party and policies and his approach to Prime Minister Jacinda Ardern would be to hold the Government to its promises, which he did not believe it could meet.
Views of Joyce are mixed among National's MPs - both he and Paula Bennett have borne some of the blame for NZ First's decision to support Labour because of their role in the negotiations team.
Joyce's credibility has also been called into question in some quarters by his claims of the $11.7 billion hole in Labour's books – although none of his rivals would directly take issue with that.
Judith Collins said it was "a ballsy call" while Amy Adams said she had not done the maths herself, but would trust Steven Joyce's calculations more than Finance Minister Grant Robertson's.
Mark Mitchell said he was firmly on Joyce's side over the hole and would want Joyce to stay on as finance spokesman if he won.