To remove bamboo your options are to either dig it out which is quite a job, or to spray it with a herbicide. However, to my knowledge there are not any herbicides that list bamboo as a controlled species on their labels. That said 41% glyphosate (Roundup is one brand name) mixed at a rate of 6 ounces per gallon is fairly effective. The bamboo should be mowed down and allowed to regrow to about 3 feet tall before spraying it. Repeat applications (perhaps 4 or more) will likely be needed for complete control. Another herbicide imazapyr (Arsenal) is as or more effective than glyphosate and is often suggested as a combination spray with the glyphosate. However imazapyr has both foliar and soil activity and is very damaging to deadly to landscape trees, shrubs, and grasses whose roots are in the treated area. Thus it is not generally recommended for landscape settings.
Another control option is to mow the bamboo regularly (at the same frequency you might mow a lawn for a couple of seasons. Such intense mowing sets it back a lot by depleting its stored energy and not allowing it a chance to grow leaves to replenish its stores of carbohydrates. Thus this technique can work fairly well at getting rid of much of the bamboo in the mowed area. Bamboo experts claim that repeated pruning of any shoots that come up for a period of time will do the trick and that herbicides are not really needed. They also recommend trenching to sever the part to be removed from any part of a grove on another property that cannot be removed. This prevents the remaining grove from supplying the underground parts on your side of the property line with energy to respout.
To keep bamboo from coming in you can trench and install a vertical underground barrier made of about two or three feet deep and extending a couple of inches above the ground. Barriers can be made of thick plastic (at least 40 mil!), metal or concrete. Slant the barrier outward at the top (away from the bamboo to be contained) to deflect the rhizomes upward. Check the barrier once or twice a year to cut any rhizomes attempting to grow over the top of the barrier.
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