If you have a choice between the smooth bark hickories (pignut, mockernut, etc) vs. shagbark hickory, go with the smooth bark varieties. They make a little better bow.
The most ideal time to harvest hickory is in August. If not August, any month that the sap is up will allow you to peel the bark off in big sheets and the growth ring right under the bark will become the back of your bow. This will save you hours of time getting the bark off and chasing a ring. August is a good month because the tree has had time for that last growth ring to reach its maximum size and the bark will still come off easily.
When I cut the log, I usually go ahead and split it into staves or billets, get the bark off and seal the end grain and back with two coats of shellac or wood glue. Put the staves in a shaded, covered area with good air flow and let them dry for several weeks before moving them inside to continue drying. Once they have dried for four to six weeks, depending on the weather conditions, I will often rough out a bow with the limbs an inch thick and 2"+ wide and steam in some reflex. To do this you want to be around 20% MC.
Several more weeks air drying on the form and then the stave or billets go into my hot box for another month or six weeks. Hickory needs to be in the 6-8% MC range to make a good bow. Get it dry. It'll be worth the wait. One bowyer I have learned from will sometimes push a stave from green to a finished bow in 60 days by using his hot box, but I don't have the need to build bows that fast.
Hope this helps for starters.
