Cut hickory once the leaves come out. By cutting early in this growing season you not only can peel the bark easily but the ring under the bark has had all winter to mature. If you wait until late summer you are using a newly laid down growth ring as your bow back.
Wood generally takes 1 year per inch of thickness to dry. When you cut the tree split the log in half then and seal the ends. Give the 2 halves a week or so then split out staves. Seal the ends and the back if you remove the bark now.
Don't let the log or staves lay on the ground for any time. Get them under shelter soon and let them start drying.
Get one stave, take it down to floor tiller stage and put it under your bed for 2 months. By then it should be dry enough to start tillering.