Before the naysayers chime in and tell you twisty stave cut through the grain will fail with a bamboo backing I can assure you it won't and is a good way to save a marginal stave.
I have backed around 30 such staves with no failures and suggest you completely flatten the back of your osage and glue the bamboo from tip to tip. Make your bamboo edges about 1/16" for the entire length of the backing, this will naturally taper the bamboo from handle to tip on both limbs.
Here is a similar stave I backed that is still shooting after a bunch of years, lots of runout but it doesn't matter with a bamboo backing.