A chlorine tub can become a bromine tub but a bromine tub can't become a chlorine tub.
As far as bleach or a floater ... Bleach can be used but will void the warranty if it is found out but with bromine you won't be using too much chlorine. I think for bromine once you put the starter in and bromine crystals you're supposed to shock with non chlorine bleach. I always thought bromine was used in a floater but my tub is 9 YO ... things may have changed.
Bleach is a type of chlorine just like Dichlor, trichlor, Calcium hypochlorite and Lithium hypochlorite. I personally use Dichlor and bleach in my hot tub and use bleach, Cal Hypo and trichlor in my pool. BUT my tub is out of warranty and so if it breaks it's all on me anyway.