I have made several bamboo backed hickory bows, I made them 1 3/8" wide. With the bamboo glued in a reflex they perform much like a bamboo backed osage bow.
If you make any bamboo backed bow too wide you end up with more bamboo back than wood belly. I made several oak and hickory ones that turned out this way early on, I called them red oak belly bamboo bows, they were mostly bamboo.