I have found that it really depends on the branch. A large branch, say over 6" in diameter, can be treated just like a butt log. It will likely have some bend to it. The best staves are usually in the lower half so it pays to mark them. The top can be good too depending on the ring characteristics. They very often dry into reflex, even if they start in deflex. The stuff from the sides is usually very reactionary and will warp like crazy and act wierd when drying and tillering.
Smaller than 6" and it's a crap shoot. It can be done but in my opinion, it is best left for after you have built several bows. There are many more considerations to building bows with small pieces. Less than 4" and I'd say you will struggle to get a heartwood bow from most of these branches. You can probably get a sapwood/heartwood bow from one but that is a lot more complicated.
I'd really like to see a bow made from anything in the 2-3" branch range. Not saying it can't be done but I have never seen a branch less than 3" with enough clean length and bow wood in it to make anything but a walking stick. It would be a rare limb indeed. Now a sucker, I have seen some pretty small ones make a bow. But suckers are special.
Have fun, make bows, or walking sticks, or furniture, or a nice campfire. Cutting osage is great fun. I cut last weekend and found a very unusual tree. I'll post pics in the next couple days.