I agree too. I think osage is a great wood for beginners. Most of the time you'll use just the heartwood with osage, but a limb that narrow may or may not have enough heartwood for a bow done that way. If there's not much heartwood, you might want to consider just carefully removing the bark and letting the outside be the bow back like you would with a white wood like hickory. Osage does like to split so take Bevan's advice to seal it seriously.
Good luck,
George