I, too, am plagued by this prolific plant from my former neighbor’s yard. However, that lot is now empty and I am on a mission to rid the land of this invasive “creature” and did some online research yesterday. I discovered two things that may help you.
First, you said that it grew through the black plastic. It might not have been thick enough and the sun still got through. Try with thicker plastic or double/triple layers. Hold the plastic up to the sun. If you can see any light, so can the plants. Also, apply some mulch over the stumps before laying down the black plastic.
Second, I read several posts that stated the only sure way to kill bamboo is to stop the photosynthesis process. That means getting rid of all the leaves on the plant. They will grow back and you get rid of those. Over several cycles, the plant will exhaust itself trying to replenish its leaves (where it absorbs sun) and die, and the roots and runners will rot. Labor intensive but sounds like the most environmentally-friendly way.
I’m going to try the latter method this spring.
I urge anyone reading this post that may be thinking of planting bamboo to realize you will have it FOREVER (and so will your neighbors), it will spread rapidly and you will have difficulty growing anything else within 20 feet of it.