Bamboo is a grass, and the best example I can give of its habits is to compare it to bermuda grass. If you have any experience with Bermuda, you will know how hard it is to eradicate because it spreads by sending out lateral stems under the soil. Bamboo spreads primarily from rhizomes (underground stems), so no, you wouldn't have it spread via bunny poop. Bermuda grass produces seeds every year, while most bamboo goes to seed very rarely (like once in your lifespan)... if your bamboo stand is very old, you may "get lucky" and have it go to seed, so just be sure not to feed the seed heads to the rabbits and you will be fine... other than it spreading via any airborne seeds it has produced, of course!