Sounds like cedar elm. It's real good stuff. You can reduce it to staves (make sure you seal the ends), let it dry a month or so, then reduce close to bow dimensions and let it dry for another few weeks. I would reduce it further to desired dimensions (floor tiller) and then let it dry some more before tillering. You can check mass at this point on a scale and she's safe to tiller when mass is constant for a few days. If you're like me, your scale isn't hefty enough to measure the mass till about this point, but it is better if you can be monitoring mass most of the drying time.
That said, i think it'll be better if you let it season for a year or so in stave form. I did both with my elm, and some of the staves took on some unpleasant bends. The quartered staves are still nice and straight.