I prefer to cut hickory in the late summer. That way the outermost growth ring, which will be the back of the bow as soon as the bark is popped off, is of near full thickness, and the sap is still up, so the bark will pop off with ease. Sometimes if you just wiggle a screwdriver under the bark at the end of the stave, it'll pop off in one big piece. Just be careful not to pry against the staves back where you may damage the bow inside. What kind of hickory are you looking at?
I cut the log in approximately 6' lengths, and either split them right on the spot, or when I get home that same day... the next day at the latest. Hickory, and other 'white woods' deteriorate rapidly if they're not drying.
You can pull the bark off the same day you split them as long as they're not stored in conditions that are too hot or too dry... or with air movement.
As soon as the log is cut into 6' lengths, seal the ends only, with 2 coats of shellac. You don't want to seal the sides or backs of the staves. You want it to dry evenly from all sides... just not the ends. The ends will check and split.
If you're in a great big hurry, you can begin working the stave down right away, it will help speed the drying process, but you should leave it 3/4 - 1" thick, and 2" wide for its entire length to allow for layout room and any warping that might occur during drying, also be sure to leave a little extra wood, in thickness (about 2") in the center 12" for the handle, flares, and dips.
Initially, and for at least the first month, allow them to rest in an area that is neither too dry, too hot, or with much air movement. A corner of the basement is good, or a cool, shaded garage.
Good luck, and keep us posted on your progress.