Were you just finding piles of old bamboo, or were you finding growing bamboo? Bamboo is not something you want to shred, it will turn into incredibly sharp splinters that will harden and resist decomposition.
Bamboo is incredibly invasive and difficult to control. If you can find an herbicide that will kill it, I wouldn't hesitate to try and wipe it out, and be prepared to battle it over the next few years. If you're diligent, you might be able to control it