I would peel the bark carefully making sure not to nick or damage the surface just under the bark as this will be the back of your bow. If the longitudinal grain runs straight on the halves you could split it again, but not necessary, could be done later. If you are looking to get started on one you can lay out your bow on the back of one of the staves, rough it out slightly larger and thicker than the desired bow. Put it in a basement or garage for a few weeks, then bring it into the house or a heated shop. Weigh it every few days when it stops loosing weight, it should be ready to work. All this being said, I have never worked ash, and assume it is handled like any of the other white woods.
I'm sure someone with more experience will be along to correct me if I'm wrong.