With woods like osage, locust and mulberry you would typically remove the bark and sapwood and chase a good, clear ring for the back of the bow. With whitewoods like maple, ash, hop hornbeam and others you remove the bark and use the ring under the bark as the bow's back. It is preferable to cut whitewoods during the growing season, when the cambium layer is active and the bark will peel off easily, exposing a pristine bow back. Your goal when building a bow is to have a back with no violations. The strength of a bow is in its back where the tension forces are.
There are some grain configurations in boards that are appropriate for bows so, even though there are grain violations from sawing the wood, they are sound enough to build a bow with a good chance of it surviving.