Mowing may slow it down, but you probably will need to use nonselective herbicides such as concentrated glyphosate or imazapyr. Multiple applications will probably be needed. Apply these herbicides when the bamboo is actively producing new growth, not when it is in a dormant state.
Be sure to check with your local Extension office (County Offices) to see which formulations and concentrations are legal to use, and as with any pesticide, read and follow all label directions.
Here is a link to the University of Florida bulletin on bamboo control: Bamboo Control.
