Are you talking about fitting a bamboo backing to a standard osage selfbow stave with a crowned back? Or are you talking about putting a piece of bamboo on an osage board? Or something else maybe?
Either way, the fit should be very, very good. No gaps.
Also, while relatively straight grained, clear wood with minimal ring runout should be used, imo, if you're backing with bamboo, violating growth rings of the osage while flattening the back is of no concern, and just part of the process.