With this common name there are generally two native species that fit the bill, Oystra virginiana and Carpinus carolinia, both in the birch family and both having very similar fruits. There is loads of Carpinus in the lower elevations where I live but you have to go up towards the mountains to find Oystra. Carpinus (also called blue beech or musclewood) has smooth bark with muscle -like undulations. One peculiar thing I have heard and found to be true is that the wood rots very fast after it falls to the ground - you'll never find an old piece laying around. I've also heard that it's a marginal bow wood.
Oystra, on the other hand has short little strips of bark that refuse to lie flat against the trunk - they point outward at the ends. This is the species that is apparently the new rage in bowmaking. The wood is very hard, very tough. Wish I could get some, but I've got to find a friendly landowner first.