There's lots of hackberry around here as well as a decent supply of ash, will either of these two white woods make a self bow ??
Yes. Hackberry makes a nice bow.
There have been lots of nice hackberry bows built over the last few years.
Both will make a nice bow - both respond well to being heat treated. One of my favorite bows is a hackberry. If you do a search on here or over on Prim. Archer you should find some nice build alongs.