It is safe to remove the bark on hickory and then rough out the bow. For osage, it is risky to leave the sapwood on after removing the bark. Safer to remove it all at once. That being said, I roughed out an osage this weekend and left a few rings of sapwood on it. I shellacked the back and ends pretty heavy. So far it is doing fine. We'll see what happens.
To dry your stave faster in either wood, make it less than 5/8" thick all the way across the stave. Leave your handle and tips full width so you can adjust your layout for any side to side motion during drying. I like to leave it in a relatively cool, moist area for a couple weeks and then start force drying in a heat box or hot area of my house.