Bridewell impressed last season, taking debutants Supersonic Racing to the Title Showdown and in the process giving BMW a first appearance in the shoot-out.
But with Supersonic having since pulled out of the British event due to a lack of backing - instead taking their entry to the Italian national championship - Bridewell was forced to seek employment elsewhere.
He has found that at Quay Garage Racing-run Bathams Honda, signing a deal for the 2013 season.
"I am really looking forward to the season,” Bridewell said. “This team is very much like Supersonic; they have very similar philosophies when it comes to racing.
"They go racing for fun and for the passion and when I am in that environment that is when I race at my best. I have my crew from last year with me again and there is no doubt in my mind that they can get that Honda working for me.
“We want even better results than last year and I want to be consistently on the podium; I want to be up there every round in 2013.
"I stand a good a chance as any of winning races this season and I want to be the top Honda rider out there. That won't be easy as there are a lot of really competitive Honda riders in BSB but I want to be battling up there with them and finishing ahead."