sure. Put the broken piece in a clear container of water. The broken piece is called the "terminal bud" when removed, auxilliary buds (side shoots) will grow to replace the terminal bud.

have fun

Bamboo is VERY difficult to kill. You can no dout propigate several new bamboo plants from the same broken piece.

Of course it does just put it in a glass of water and wait for two weeks to go by then your bamboo shoot will have new roots appearing, then put it in water with rocks in it, they need clean tap water in order to root, i have tried water from a lake and it did not work, then i tried tap water then it rooted, i have done this for a year mine keeps on producing shoots so i root them in clean water. I hope this helps and Good Luck!