Well, other than the band saw part where I suspect he was kidding, New Indian is right on. With osage the common approach is to remove the bark and white sapwood and use one of the yellow heartwood rings as the bow back. The common tools for this are the draw knife and scraper. It is a lot of work, but with experience it can be done reasonably quickly. Your first attempt is going to go slowly though. Most people I teach get comfortable with the process in a couple hours and finish their bow back in 2 or 3 sessions of about that length. Subsequent bows they do faster. It's much easier to demonstrate than explain. Look for youtube videos on osage bow building, most will show at least a little of the process. If you're near Dallas, come to my shop. I've toyed with doing a video just on chasing a ring, but never have. By now there's probably one out there.
One other thing. Once you've exposed a few inches of heartwood, seal it with some shellac. Even long cut osage can have enough moisture in it to check.
Good luck,
George