Bridges' new office is on the ground floor of Parliament House, as far away from the Leader of the Opposition's office on the third floor as possible.
Muller declined Bridges' request for foreign affairs and Bridges turned down the offer of the justice portfolio.
However, Muller did say Bridges would be in the shadow Cabinet if Bridges decided to stay on as an MP - something Bridges had quickly announced he would be doing.
Bridges acknowledged Muller was not willing to give him a position he wanted.
"I'm sure we'll keep talking and, certainly, as someone once said 'I'm happy to be the member for Tauranga.'
"It's always, whether I've been a Cabinet minister or Leader of the Opposition, been my most important role. I've now got more time for that.
"That said, in the future if I can play a more significant role I'd be open to that, but we'll just see where we get to."
Bridges confirmed he still intended to stand for National in that electorate at the election.
Asked how he thought the new leadership of Muller and deputy Nikki Kaye had performed over the last week, he said that was a matter for them to talk about.
"But I want to be a fully contributing member of this team. I'm glad to be back, this is an important place like no other and I believe I've got a real role to play here."
He said the last week at home had been "restful."
The most high-stakes contest he had entered had been board games with his children - contests he was clearly determined he would not lose.
He had played board games Risk, Stratego and Rat Race with his sons Emlyn and Harry.
"There were a few tempers from the boys as they didn't go so well.
[Children] Emlyn, Harry and Jemima have enjoyed it. Bits of it anyway."
Bridges also again voiced his view that New Zealand should move out of lockdown as soon as possible.
He said he had always supported the right to protest, whether or not he supported the cause. "And here I understand the cause very well."
However, he said it did seem ridiculous that the protesters were allowed to gather, yet people at churches and businesses could not.