I would definitely put down a membrane, which requires trenching down almost 3'. Or you could dig a 18" trench and filling with sand, and check twice a year for rhizomes. If you're careful you should be fine. Probably.

I am bumping this because I have a very similar situation, and I, too, would like an answer.

Membrane (barrier) only needs to be about 9 inches deep, maybe 12 to be safe

Darn, I was really hoping to hear that I wouldn't need a membrane. At this point, I would have to basically destroy my little garden to install a barrier, so it's not going to happen. I haven't seen any new shoots since I planted the bamboo about 6 weeks ago, but I imagine next year when it's well-established it will send out runners every which way. I will probably resort to just clipping them off if they spread too close to the fence line, and digging down to catch any run-away shoots.

I have read they can send runners up to 12 feet across under asphalt.........as in bamboo on one side of the street and runners coming up on the other side of the street.

I have three running species in a 6 x 60 raised bed. Rhizome pruning has kept everything in check so far. On one side there is no irrigation and it is hard clay. I'm not going to prune that side this year and see if anything even shoots. Other side is lawn w/o irrigation. I rhizome prune in the fall and I've had a couple shoots in the spring. I just go back and reprune that area and mow the shoots.

While digging a drainage ditch about six feet from the bed, I dug up one dead rhizome that had been pruned in an earlier year. It had no feeder roots and had never sent up shoots. In my climate, this regime seems to be sufficient.