2" diameter bamboo actually gives you lots of options, as well.
Also, don't think in terms of BIG trees, yet, unless one falls in to your lap. Look for thickets of small trees growing close together and find a tall, clean, mostly branchless sapling, not twisted or leaning, 5" in diameter or smaller, 3-4" is perfect. Hickory, maple, ash, elm, black locust, cherry, hawthorn, plum, hornbeam, and mulberry often grow like this in clusters. Look DEEP in the thicket, where the older forest opens or clears. Such a stave will get you a nice flatbow or BITH of hunting weight.