Once the staves are split there is no reason to remove the bark until they are dry. I'd give them a few months at least. This is not to say you can't make a bow sooner with one or two of the staves but for the majority I'd give them at least a few months. Being split(sawn) the moisture has a place to escape and especially when wrapped together with the spacers between the two halves.
I've used this method twice with osage on 2" to 3" diameter poles. The first time I sawed the osage pole in half and let it dry. Both halves drew up with 6" to 8" of backset and twisted. It took a lot of heat toi get them to reasonable staves to build a bow and on the one I tillered out, it developed a crack across the back because of the excess stressing just pulling the stave outof reflex and into deflex as I tillered. On my most recent attempt I gave the poles about 2 weeks to a month before sawing it in hlaf(with the bark left on). Once I did that I bound them together with small spacers between the two and left them like that foe a few months before unwrapping. After unwrapping, both drew into a small amount of reflex but were relatively straight without twists. When I get around to building a bow I will add reflex is it is needed and if it is needed.