Bamboo preforms best as a backing for hard, dense woods like osage, ipe and other tropical woods. IMO
I have seen good boo backed red oak bows and boo backed hickory bows but why go to the trouble of making a boo backed bow(they are a lot of trouble IMO) and use not so strong in compression belly woods.
When building wood bows, no matter if they are selfbows, backed bows or multi-lam bows you have to consider the tension qualities of the back and the compression qualities of the belly because that is where the stresses are. Most woods, if not all, are stronger in tension then they are in compression with some being very strong in tension(like hickory, osage and others) and others being strong in compression(like osage, yew, ipe and other tropical and domestic woods). When using boo backings I want to use strong in compression woods for the belly. For less strong compression woods like red oak a backing of hickory, maple, elm or ash would be more appropriate...or paper, silk, rawhide or linen just for protection.