I got more info on this. Using bamboo to back a bow is a good idea, but using bamboo flooring is entirely different. I just wanted to document that in case someone else stumbled across this thread and filed it away as useful information. Bamboo flooring is very pliable and strong by itself, but when it is the outer lamination (the back of a bow is what most people might consider the fron - the outside of the curve) it tears easily. Raw bamboo (cut from a large diameter stalk) is much stronger.
I ended up getting a couple of pieces of oak flooring, one rift and one QS, out of the dollar bin at the ReUse Center in Raleigh. I planed the faces, wet out a 2" strip of fiberglass tape with epoxy and sandwiched it in between. Once I get it cut down to form, I will put another strip as backing over the QS oak. I don't understand all the reasoning, but apparantly rift sawn is preferred in compression (inside the curve) and QS is preferred on the outside. The fiberglass isn't required but substantially reduces the chance of splitting/breaking.
I still would like to get some hickory, but according to some info I got from a bowyer's board, a perfect piece of oak is actually better but the tolerance for imperfections is much higher with hickory; you can get away with more runout.