True bamboo is very much like a grass. It does grow very quickly, but in spurts, between which it appears to be storing up energy for another rapid growth phase. Bamboo needs a lot of nitrogen to be healthy. You can use a lawn fertilizer or slow release fertilizer that is heavy in nitrogen. Bamboo can be propagated by separating the culms if it is a clumping type or cutting runners if it is a running type bamboo.
To keep it dwarfish, you need to constrain the growth in a pot and pinch out a portion of the growing tip.
here is some information on
bamboo cultivation
"Lucky Bamboo" is not a true bamboo. If you click the search bar above and enter lucky bamboo, you'll find some info and links on that subject, too.
Regards,
Matt