The only "ash" I know that makes a lousy bow is what americans call mountain ash, which is actually rowan and not an ash at all. Green ash should make a fine bow. It makes a nice electric guitar body as well.
I have to help my father cut a bunch of ash that's infested before the spring beetle hatch, both white and green. PA's ash is getting hammered hard by the little buggers. There will definitely be an ash shortage in our future. Here's hoping mama nature did her job and at least a few are immune to the fungus the beetles carry.