Bridges took the call in the Koru Lounge at Wellington Airport this morning. Obama was with Key at the time.
Bridges will attend a dinner and speech by Obama tonight but with more than 800 likely to attend, a chance to chat could be difficult.
Prime Minister Jacinda Ardern will meet with Obama this afternoon.
Obama will be offically welcomed in Auckland today with a powhiri by iwi Ngāti Whātua-o-Ōrākei at Government House.
Ngāti Whātua-o-Ōrākei, Whai Maia, chief executive Rangimarie Hunia told Newstalk ZB it was an "absolute honour" for the iwi.
"We see him as one of the most influential leaders on the planet. To have the opportunity to welcome him in our traditional language, through the eyes and heart of our culture, means a lot to our people.
"We hope we can do the nation proud."
He will then have a meeting with Prime Minister Jacinda Ardern, who was remaining quiet about what she would discuss with him yesterday.
Obama's main event will be a dinner and discussion with actor Sam Neill tonight in front of 800–1000 guests at the Viaduct Events Centre.
That meal has been chosen and overseen by chef Peter Gordon, who was flown over from London by Air NZ for the occasion.
Gordon told 1 News he was told Obama liked fish so had selected New Zealand salmon as one option and steak for the other "because he's from Chicago".