I use rawhide a fair bit as a backing, mostly on whitewood boards. Just recently, I've changed (for the better) the way I apply it. I used to glue it on after cutting the bow's profile, but not anymore. Here's what I do now:
I soak the rawhide in cool water until it's completely soft and saturated. Let it soak until it's all the same thickness. Some parts are a bit thicker, and may take longer to soften. This is usually done in about an hour. I take the rawhide out of the water, and lay it on a big towel to dry. I use TB3 to apply it... it's waterproof, cheap, and cleans up with water. Apply glue to both surfaces... rawhide and wood. If you let the rawhide sit for a bit, it's less saturated, and the glue doesn't become so thin and messy. Remember to apply glue to the flesh side of the rawhide.
What I do differently now, is sandwich the rawhide between two layers of board... the one I'm gluing it to, and the other as a compression and clamping layer. I'll make the wood I want to back the same width as the rawhide strip, usually 2", and the clamping board the same. I put a layer of wax paper between the rawhide and the clamping board, so it doesn't stick to it. I wrap the entire thing with bicycle inner tubes, leaving a good inch space between wraps. Don't wrap it too tight... I use about half the pressure I'd use than when gluing wood backings. I let it sit for a minimum of 24hrs. After, I'll draw the bow's profile with pencil on the rawhide backing, and cut it out from there. I've found this method results in less edge lifting of the rawhide. Once the bow is cut out, I round the edge off with sandpaper, and start to tiller the belly. Keeping in mind, this is for a board bow... a stave bow is a whole other thing.