When bamboo truly gets out of control, all measures to remove it range from difficult to very difficult. There are basically three acceptable approaches, and one that should be avoided.
The American Bamboo Society's official position is: "If you must remove unwanted bamboo, the only truly effective way to get rid of it is to dig it out. The ABS does not recommend using chemicals to kill bamboo because of the potential for environmental damage from ground and water contamination and the potential for contact with humans and animals." However, be warned that digging out bamboo can be REAL work. Don't even try until the fall rains come to soften the ground--digging before then will simply result in breaking off the canes, and the roots will definitely regrow. And even under ideal conditions you will be chasing escapees for several years.
The English equivalent of the ABS is the Royal Horticultural Society's bamboo group, and their official advice is more chemical-friendly: "[C]ut down canes to soil level in late winter and then apply a glyphosate*-based weedkiller; Alternatively, cut canes to ground and treat with a stump and root killer containing glyphosate." If you go this route, be sure to read and follow all directions on the label. Glyphosate is among the more benign herbicides, but it should always be handled with care. (Weedkillers are frequently a "cocktail" of several chemicals, most of which are more hazardous than glyphosate, and for this plant straight glyphosate works better than the mixtures). Also note that the weedkiller must be "painted" on the cut stems (generally a household hand sprayer works better than a brush) within 2 minutes of making the cut--for some plants that window is closer to 20 seconds. So the technique is cut--spray--cut--spray. Be aware that this is not a one-time solution--you will see shoots reappear for three or four years.
Third, you can starve the plant to death, by cutting down all foliage as often as it reappears. This can actually work very effectively, as the plant uses energy to send up new shoots, which you are removing before they can recharge that stored energy. However, this strategy fails if you neglect to keep cutting. And since the various shoots are all connected to the same root system underground, failing to cut in one area can recharge the entire root system. (Note that where possible, simply running the lawnmower over new shoots is a great way to eliminate new growth.) So this alternative is chemical-free, and probably less labor intensive than digging, but requires continuous ongoing diligence, over the same three or four year period.
The one strategy that is NOT recommended is spraying pesticide on the leaves. The only recommended herbicide--glyphosate--will also kill most other plants if it gets on their leaves. So spraying short bamboo wipes out your lawn, or the desirable plants in your beds. And spraying tall bamboo wipes out plants all over several adjacent yards, and can present a serious health problem to innocent bystanders of all species. Do NOT try to control bamboo by spraying its leaves!