It's pretty light, meaning high accelerations on your passengers in the event of a crash. Probably flammable, too. Your crash safety ratings might be unacceptably poor.
How well does it tolerate heat and vibration? There will be places where bamboo is next to vibrating engine mounts, and others where it might be near hot exhaust lines. What happens to bamboo exposed to oil? Does it dry out and crack when exposed to sun for long periods? (Can you mitigate that by treating it, or applying a coating?)
Does it expand or contract a lot when aged, or heated, or cooled, or wet? (I'm wondering if your frame is going to deform when the weather changes.)