That's a lot of root barrier to put down. I found some documentation from Fairfax county Virginia on how to properly contain bamboo and they suggest a 36" deep barrier (30" underground) for containment and a concentrated Glyphosate/Triclopyr application to cut surfaces for herbicide control. I'd probably take a belt and suspenders approach and place both a proper barrier as well as treat aggressively with targeted herbicide applications to keep it out of your yard, as it sounds like your new neighbor doesn't really care. I'd also look to your local code enforcement office to see if they have any suggestions.