Can bamboo penetrate fibreglass?
The roots of rhizomatous bamboo are soft and will turn away from / run along any barrier they encounter, so damage to the pool isn’t very likely. The best long-term solution would be for your neighbor to install a minimum 2 foot deep plastic barrier along their side of the fence to keep the shoots from invading into your side. Failing that, install one on your side as close to the fence as you can.
