I've made a few bows from infected/dead elm. Works fine depending on how far along the disease has come. If it's early on, it works. Then it's just the outermost 2-3 rings that are affected. Remove those infected rings and you've got healthy wood underneath. I'm not sure, but I would even guess that the infected outer rings are good as they are, given, again, that it's early in the process and no real rot has begun. That's just a guess, but the infected wood still feels quite strong when you cut it off. Probably differs from tree to tree though.
So the answer is, you probably got some decent bow wood right there. A little more work than what elm usually needs, but good nonetheless.