With a tension strong wood like hickory or elm, a 3" sapling can make a bow(ok, not a wide bow, but a bow). Always cut live wood or a tree that has fallen less than a week or so ago- white wood, such as hickory, elm, oak, birch, ash, etc rot fast and quickly become useless.
Go with something from 5-12 inches(IMO anything bigger is a beast to cut and split... 6 inch elm is a PITA) according to TBB Vol 1.
Try to find something about 70" long, 8" diameter. Cut it carefully, and IMMEDIATLY AFTER YOU CUT IT, paint the ends with glue or sealer so it doesn't crack(check) as it dries. Peel the bark off for hickory and most other woods, but not for Osage or Locust. Don't cut into the wood under the bark- it will become the back of the bow and must have a single ring.
(ok, enough rambling)