I know it sounds obvious, but I would ask your neighbor what kind of bamboo they planted. Chances are it's a runner since that's what most nurseries sell. I wouldn't worry about the pool cement, the worst it will do it find and exploit cracks in the surrounding cement. My advice is to act now, because once spring time comes it may be too late.

It sounds like you've already fallen into the trap of believing the urban legends about bamboo and getting spooked. Even if it is running bamboo, it may never spread your way. If it does spread your way, all you need to do is to take a sharp shovel in the middle of the summer and the late fall and chop off any wayward roots, and pull them up. They are usually within 6" of the surface. If you do this regularly, you will not have a problem. Bamboo cannot regenerate from an amputated root unless it has been given time to establish itself. Now, if you don't do this for 5 years or more and let it move in, then it may cause a problem. But despite what you may have heard, bamboo is not going to invade and destroy your pool.

It may seem unfair to have to do anything because of your neighbor's plantings, but it's really no different than if he planted trees along the property line and the roots came into your yard. You or he could always put in bamboo barrier along the property lline, but that's a lot of digging (24"-30 ditch) and doesn't always work. In my previous home I had a small grove of bamboo that never expanded much in 30 years. At my new place I've got over 50 kinds of running bamboo planted in my yard without any barriers and I have yet to have any escape or attack me at night when taking out the garbage. Take deep breaths and relax...

Thanks for the info. I didn't want to panic, but I have heard about problems in trying to control bamboo. My neighbors aren't gardeners by any means, so I can't imagine them putting in any effort to prevent the bamboo from spreading onto my property. I know they're just looking to grow a privacy barrier.

diana-
If you can give me some more info, I'll see if I can give you any more input.

1. What part of the country do you live in (Zone)?
2. What species of bamboo?
3. How close to the property line?