Osage doesn't rot like white woods do. However, the wood that lays on the ground may still be quite green. If you have borers there, the wood will probably have them. Where I am in Texas it takes awhile for borers to get into the heart wood. Most stay in the sapwood. However, my untreated 3 year old wood has some deep ones. Even so, I have yet to not be able to make a bow out of a piece. To me, they're an annoyance. I just go deeper in the heartwood to make bows. There's no rule the top heartwood ring has to be the bow back. Lately I've been going down 5-20 rings. It isn't even any slower for me. You can hog off extra wood very quickly if it's relatively clear of knots. I'd bring home every bit you cut, unless it's just too crooked.
George