Round-up will work on the emerging stalks, but won’t stop his plants from continuing to send invaders burrowing underground. I live in Oregon where blackberries spread aggressively, with thorns no less. I had several major patches in my back yard when I moved in a few years ago, some coming from under a neighbor’s fence. My best strategy turned out to be cutting it down little by little in lengths I could manage and get into my yard waste can – when I got to the point where I was cutting it off at the ground, I sprayed Round-up on the freshly cut root. That way I wasn’t randomly killing surrounding plants and my guilt over using toxic chemicals was lessened by limiting the amount. It worked pretty well, but I have to be vigilant – a couple times a year, I have to repeat the process with some volunteers to keep it from taking over again. There must be some deep roots with eternal life :-).
Anyway, I just googled bamboo depth and barriers have to be 24–30” deep to keep bamboo from burrowing underneath! And they said if you use concrete and it cracks over time, the bamboo runners will push through the crack. No way should you have to be responsible for the time and expense involved in dealing with this, IMO. Especially since it’s damaging your house.