Although bamboo is often called a tree, it is actually a form of extremely tall-growing grass. Because it's a grass, bamboo can spread by runners, just like the grass on your lawn. Bamboo is often planted as an ornamental plant, but if you don't take steps to keep the plant in check, through mowing and removing new bamboo crowns as they spread, the plant can soon take over. The only way to stop bamboo from growing is to kill the plant completely.
Install a barrier around bamboo to contain it by digging an 18-inch deep trench around the bamboo grove and pouring concrete into the trench.
Continue to monitor the bamboo grove after containing bamboo. Bamboo runners are prone to creep over the tops of barriers. Cut back any runners you see emerging over the top of concrete barriers.
Mow new bamboo to the ground as it begins to grow. Young bamboo is succulent, and will mow down easily. Repeated mowing will eventually kill bamboo crowns.
Cut down older, woodier bamboo with an axe.
Paint the tops of cut bamboo stumps with a systemic herbicide containing glysophate. The vascular system of the bamboo plant will pull the herbicide down to the roots to weaken or kill it. You may need to treat bamboo repeatedly to kill the crowns of the plants.
Dig out bamboo crowns from the ground with a shovel, mattock or grubbing hoe. If you choose to dig the plants out, you must dig up all of the roots. Unless you remove the complete bamboo crown, the plant will continue to grow.