Red elm is pretty good bow wood, as is American elm (White elm). Personally, I like Red Elm better. It splits way easier and is in general way easier to work. If you get some Red Elm, use the wood directly under the bark for the back of your bow. In my experiences, the sapwood makes better bow than the heartwood. Winged Elm and Rock Elm I have heard are also very good but I have never tried them and don't know anything about them.
CP