Why do you want to use bamboo flooring as opposed to 'normal' boards of oak, ash, hickory etc.? I don't see why that would be better. Those floorings are only 36 inches, which is too short for a shortbow. You'll have to splice them, as Prarie mentioned. Furthermore, these flooring boards have a thin (approx. ¼") top layer. It's not solid bamboo all the way. It's usually a thin top layer glued down onto more bamboo (glued perpendicular to the top layer) or plywood. That means you have to remove that base layer, since only the top layer is useable. Those thin slices of bamboo are excellent cores in laminated wood. But their grain is too violated to use them for a backing, and the stuff is also not good in compression. For tillering practices it can be used, but I don't see why you would want that, knowing that the bow will be shortlived and knowing that you can also practice tillering shortbows on other species of wood, that will be more succesful.
However, for your application, the biggest drawback will be the limited thickness of the layer of bamboo.
By the way, make sure you get the side pressed bamboo, and not the plain pressed.
