Cut the bamboo down a few inches above the ground with a pair of garden shears. This will make it easier to access the rootstock.
Dig into the ground a few inches. You don't have to make a wide hole. One that extends out an inch or two from the bottom of the bamboo will give you good access to the roots. Also, clump bamboo rootstock is quite close to the ground surface, so you will see it soon after you dig into the soil.
Pull out all of the rootstock and any additional shoots and discard them. This is the only way to prevent the bamboo from re-growing.
Dig out as many underground stems that you can access. This could be an extensive project, depending on how much the creeping bamboo has spread. Fortunately, the underground stem (rhizomes) stay fairly close to the surface, so you shouldn't have to dig too deep to access them.
Remove the root mass. If your bamboo has significantly spread, you may need to rent an electric rototiller to dig up to 18 inches deep to access the root mass. When you get to the root mass, dig it out with a shovel and remove any additional stems.
Spray any dead rhizomes in the winter with a product containing diclobenil. Be sure to follow the application instructions carefully as different brands require different spray amounts per area. The diclobenil should prevent regrowth, but if you notice new sprouts in the spring, you will need to spray them with a glyphosate product. Continue treating the new sprouts throughout the growing season whenever you see them with a glyphosate product, and make sure to follow the exact instructions and warnings on the product's label.