I would repair that by soaking the fracture with thin c/a glue, maybe even bend the bow a little to open the wound so the glue finds the bottom. then, lay on two courses of silk fabric in c/a glue, extending an inch or so above and below the fracture and down the side of the limb nearest the fracture. then, wrap the ends and middle(directly over the crack) with rod-wrapping thread or similar thread, also soaked in c/a glue. this is a very strong and reliable repair. another nice thing about it is that you can sand it when it's dry, so you can feather out exposed edges. so, it isn't too horrible to look at when it's done if you take care while doing it. you could also back the entire bow this way without affecting tiller.
applying hickory or bamboo backing isn't repairing your bow, it's rebuilding it, but that is certainly a good option, too.