How do I get rid of bamboo, invading me from my neighbour's yard?

I gasped when i read that! To be honest, you might just have to get used to it. Pull them regularly, could be every day for as quick as those suckers grow. Anything that would potentially kill the bamboo will kill everything else too. I'm sorry. I wish I had better advice you 😢 my mother In Law had some that came up under the fence from the neighbors, my nephew did something to it to get rid of it (I don't remember what he used, something like roundup) but it killed an apricot tree and the bamboo was back in less than a month. Again, I'm sorry

The best answer is to cut them down and apply full strength Round Up to the fresh cut. But that isn't a sure way to kill them. Sorry no easy answer.

There are two basic types of bamboo, clumping and running. The clumping types get wider each year but they are not invasive. The running types send out rhizomes that can come up quite far away from their origin. This spread can be managed by mowing, but to stop the spread of rhizomes a physical barrier must be dug into the ground.

Companies that sell bamboo also sell barrier material to control the spread. For your situation you would need to dig a 2' or deeper trench along your fence line, cutting through and removing any rhizomes along the trench. The barrier material is high-density polypropylene at least 60 mil thick and a minimum of 24" tall at a cost of $50 for 25'. More often, 80 mil 30" tall material is recommended. https://lewisbamboo.com/category/bamboo-shield/

I would dig a trench along the fence line and dump in some strong herbicide to kill them and a piece of metal to prevent them from creeping back..... https://www.gardeningknowhow.com/ornamental/foliage/bamboo/kill-bamboo.htm

Digging it up. Surrounding trench, pouring vegetation killer, rock salt in the trench and any new growth.