Answer: Bamboo is basically a giant grass, so you can visualize how it spreads through roots and rhizomes. Not all bamboos are invasive, but the running types of bamboo have root masses that travel 3'-4' deep, and spread 15'-20'. You can starve the roots by keeping the tops continually cut down. If you're persistent the plants will eventually run out of energy to produce new canes because there's no above-ground photosynthesis taking place. However, since the tops start in your neighbor's property, you'd have to wait for them to actually appear in yours. Since the bamboo is destroying his pool, perhaps he is amenable to removing it before it gets truly out of hand, and offering to assist with this project might make it more likely. Although you probably don't feel like it's your responsibility, it might be easier/cheaper than trying to deal with bamboo invading your space as well. Digging the roots is the only sure-fire way of eradicating bamboo. You might be able to speed the process by covering the soil with black plastic after cutting down the tops of the plants. If the area gets a lot of direct sunshine, the ground will heat up, basically killing the roots. Leave the plastic on for 4 to 6 weeks in the midst of summer heat/sun. Chemical herbicides are least effective; they may kill the tops of the plants but the roots are hardy and will send out new shoots. A root barrier along your property line might be an option, but since bamboo roots go so deep, this can be problematic and expensive. They'd punch through the landscape fabric barriers eventually, and a concrete (or similar) barrier would also prevent your plant roots from spreading and be problematic for other projects in the future. It's a difficult situation. We don't have the ability to advise on legal matters, so you'd need to check with local zoning authorities or a lawyer who deals with property issues. Good luck!
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