Bamboo is an excellent barrier plant, spreading consistently through underground rhizomes. It doesn't need a lot of care, just enough water to store in its rhizomes for making it through dry times. It is this versatility that makes bamboo a stubborn plant to kill. Even though you might cut down the bamboo, there is still a lot of energy stored up in the roots that will send out a flush of new growth. If you use a combination of several methods of control at once, you should be able to permanently remove bamboo from your yard.
Remove all the standing bamboo. Wear gloves and eye protection as the bamboo can be very sharp to work with. Cut it down with a chain saw or pruning loppers or a similar sharp tool. Get as close to the ground with your cuts as possible.
Spray the area with a broad-spectrum herbicide (glyphosate) to kill any emerging growth. Make sure you apply it when the area is dry so dew or rain does not dilute the product. You might have to apply it once a month whenever you see new growth showing up. However, this method of removal is slow and not usually effective without multiple applications.
Remove the top 6 inches of soil for very stubborn stands of bamboo. A regular garden spade will work but if you rent a tractor with a shovel, the job will go much easier than trying to do it manually, but it will also make a mess of your yard. Most bamboo grows within 6 inches of the surface of the soil so by removing the soil you will remove all the rhizomes sitting beneath the surface.
Cover the area with a sturdy brand of weed matting or cloth. This will form a barrier to keep any bamboo sprouts that you might have missed from coming up and getting started again. Place 6 inches of topsoil or mulch over the barrier and plant your new landscaping on top of it.