Is it black cherry you have? That is not the same type of cherry bark used for bow backings. Even if it is the correct cherry bark you want to add cherry bark to a bows back and not use the bark that is on the stave. If that bark does crack under tension it will crack down into the bow, ruining it.
The cherry bark that works for bow backing grows around the trunk of the tree and is thin and very strong. Other cherry barks grow up and down the trunk like most other tree barks do and is thick and brittle.