This is a problem that could require heavy equipment, or better, a contractor. There is trencher equipment that is used to dig deep narrow trenches in the ground (Ditch Witch is a common brand in the USA; search that to get an idea of what I'm talking about). After digging out as many roots as you can find, contract a trencher to dig a trench (2 ft deep if possible) and install that continuous plastic barrier material.
I have bamboo in my yard. It is both a blessing and a curse. It provides me with many tomato stakes, etc., But it is terribly invasive. I go around my woods with a machete, loppers, axe, and lawn mower to get rid of as many growths as possible, leaving some in one corner of the yard. It has invaded from a neighboring yard.