Bamboo overpowers bellies for the same reasons intact wood backs overpower bellies. It is very strong in tension, but so are most bow woods anyway, like the intact back of a hickory, elm, maple, or mulberry sapling. Designed has a lot to do with it. Thinning and trapping the boo pretty far on a lighter wood is a good idea.
So you can use a lot of woods. I have made a LOT of bamboo backed bows with the bamboo flooring, and woods as light as red mulberry heartwood, plum, black locust, jatoba, etc. Also, had good success with very elastic woods in compression like yew heartwood, ERC, and juniper.
BUT, I definitely think you'll be better served pairing it with a high quality dense wood. Osage orange is fantastic, and ipe and massaranduba just as good or better. Brazilwood was pretty good, too.