Like any bow wood, the longer(to an extent) the better.  I bought a stave from Yazoo's Dad at Hickory NC 2 years ago that was cut May 8. The shoot was at the end of May and I had a 60" bendy handle static recurve built and shot in a month later. That bow developed frets and I am convinced that it hadn't been seasoned long enough(or it could have been my tillering  

 )  I know folks that have been successful with quick drying osage.
  You can reduce a green osage stave to floor tiller stage, seal the back and let it dry well without adversely affecting the stave. It will dry quicker that way.  However, there is a big difference between a dry stave and a seasoned stave. Seasoned staves fair better as bows.IMO