Putting a trench around the grove will not necessarily kill off all the roots that extend beyond the trench. The ones that are relatively new -- say 6 months old or less -- will probably die. However, those that are older can support themselves. However, this is not a big deal. When you see new shoots coming up, don't just snap them off since the rhizomes will continue to spread. Instead, simply dig up the rhizome all the way back to the trench line; it will probably be within 6" of the surface, and its fairly easy to use the pointy end of a pickax to expose the rhizome and pull it out without doing much damage to your lawn. After doing this for a year or two, it should mostly be gone. It's not going to go wild and engulf your yard if you do a little basic maintenance for a while. I have a lot of bamboo -- some with barrier and some without -- and I do this operation annually to control wayward rhizomes.

One thing I want to be clear on is what your perception is about this problem. Are you worried that somehow the bamboo will damage the house or the foundation? If you have a crawl space and the rhizomes reach it, then you will want to get under there and take them out simply so that they don't get established and then send out more rhizomes in all directions. However, they are not going to damage your foundation or your underground pipes, or crack your slab, etc. I've had bamboo groves growing right up against my perimeter/slab foundation for years and it's just not an issue.