Lets see, it's very crooked, and has thorns. Yep, that's osage. The wood will be a yellow-orange color with a thin ring of white sapwood just under the bark. The hard part is finding one that has a straight section long enough to make a bow from. Look at the bark and try to find one that doesn't have any twist to it. And the thicker the growth rings the better. You want thick dark rings and thin lighter colored rings. When you cut one, seal the ends with glue, shellac, or polyurethane as soon as you can. I seal the ends as soon as the tree hits the gound. Then you get to the fun part, splitting it and removing the bark and sapwood.
Hickory is also another good bow wood as JW mentioned. Especially if you are in a dry climate like texas.