I have only worked with green osage so far and now it is drying.  I chased a ring on most of my staves but not nescessarily the one I want to end up with.  It was rather easy to chase rings with green wood but my question is how will that change when the wood dries?  Do I need to go back and chase the ring that I actualy want now or just wait untill I am ready to build the bow?

I have better luck chasing my final ring dry.  The early wood seems to crunch easier.

There's no reason to do it now, it will chase the same when it's dry. I really can't tell a difference myself, but some of the others that work with Osage may have a different opinion?

Did you seal the ends and the back of the stave leaving the belly unsealed? If not, you should seal the back so you don't get any splits in it.

I always chase the final ring when it is dry for the same reason that bigcountry said. To me its pretty easy to go too deep and cut into another ring when the wood is green.

Thats what I wanted to hear.  They are sealed and I will wait till they are dry to chase any further.

Does the same apply with Hickory??  Is it easier when its dry?

I do the same thing. I. E. Chase to a ring or two obove my final and let it dry. After I heat it all the way I want I remove rings down to my final ring. The extra rings give some insurance from abuse and heat.

I have never worked hickory so I can't help there.