Lead guitarist Richie abruptly left the group in the middle of a tour in 2013, reportedly because he wanted to spend more time with his daughter.
The It's My Life hitmakers, led by frontman Jon Bon Jovi, pressed on without him, recruiting collaborator Phil X to fill the void, and Bryan reveals the line-up change gave the group a new lease of life.
"It's a different thing, but there's new life, and I think when you have new people, you have new energy," he explained to Antiheromagazine.com.
"Of course, we had some wonderful years with Richie, but if he wants to move on in his direction, it's one of those things that you can't avoid."
Bon Jovi will release This House Is Not For Sale, its first full studio album without Sambora, on Friday (04Nov16), and Bryan insists fans will be able to hear the renewed energy of the group on the new project, which also features old producer and guitarist John Shanks.
He continued, "The premise of this record is the roots and the fact that we're still together and strong and love playing music together... That completely was the theme of this record, going into the studio, taking the songs, playing it together as a band, changing it around. Everybody can pitch in, and everybody would transform it into something else. So, it was truly collaborative."