With woods like osage, black locust and mulberry seasoned is the way to go. You can build a bow with these woods just dry but you will get better performance, more stability and less set with seasoned wood. I don't make many whitewood bows but I think you can get by with dry wood using whitewoods. Get your wood down to floor tiller stage and it will dry quicker. Keep it in your house with A/C and it will dry more and stay dry.
I don't use a moisture meter or weigh my staves but I've collected wood for twenty years or so so I always have seasoned wood. I think that is the way to be sure your wood is ready to work, by collecting wood for later use instead on finding one stave to work on. If you are cutting one stave you can cut 4 or 5 with just a little more work. I can tell by the sound of the tools as I work the wood and by the feel, how does the wood recover when bent. If the wood feels sluggish when you bend it it probably hasn't dried or been seasoned enough. And, just because a piece of wood has seasoned for years doesn't mean it is dry enough to work. The moisture in your wood goes up and down with the R/H in your area. That's why I do most on my bow building in the winter, the R/H is generally dryer then.