Eliminating an existing stand of bamboo is a two step process.
Cut all the stalks to the ground and allow the new growth to emerge and develop leaves during the summer. In October spray the mature foliage with a non-selective herbicide containing glyphosate. (There are some glyphosate products labeled for bamboo). Repeat the application in 14 days.
Follow all label directions and be careful to protect non-target plants from any over spray." This may need to be repeated for several seasons. Bamboo is semi-evergreen and has a waxy coating on the stems and leaves, so a surfactant (helps the herbicide stick to the leaves) is advisable. If any bamboo is left alive, it will return. See our bamboo publication http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG28%20Bamboo.pdf