Is your hickory a stave or a board? Hickory is tough wood. If it is a stave, no backing is needed...probably! If a board, A backing might not be necessary. It all depends on the grain on the back an side of the board.
Is the ash you have black ash(Fraxinus nigra)? If so, I've heard that it and blue ash(F. quadrangulata)are not good for bows. Black ash is used for basket making. One method of getting the weavers is to beat a log to loosen the rings so they could be stripped off to make the baskets. If the rings strip like you said, I would be leery of it as bow wood or backing. Pat