I am not sure if you can. Some bamboos are very invasive and persistent. Would your neighbour do something aboutnit their side....i.e. remove it?

I think it's going to be an on-going battle and you will have to pounce on every new shoot and dig out roots where possible. Have you spoken to the neighbour about it? I'd be inclined to invite him round for a drink so he can see for himself what damage his bamboo is doing!

If the neighbour cannot/will not remove it (and it sounds like it will be difficult to do so). A concrete barrier about 50cms deep and 5cms wide will stop most underground bamboo shoots - you can do that up to the boundary. You can easily remove the overground shoots.

The underground rhizomes travelling from your neighbour’s side need to be severed. They are usually found within the first few inches of soil, but may be up to a foot deep. If you press a good spade firmly into the soil along your garden border, it will hopefully sever the rhizomes coming over your side. And then you can dig out anything already on your side (or if not possible, just keep cutting off any emerging culms until the plant dies over time without its leaves).
Hopefully your neighbour may offer to do all of this, once you show them the situation. Then they could keep their rhizomes on their side in the future by doing the spade cut technique twice a year - or for a more permanent solution, they could install rhizome barrier on their side.
We bought ours (about £4 per metre) from Jungle Giants:
http://www.junglegiants.co.uk/acatalog/Rhizome_cBarrier.html

The barrier needs to be angled with its bottom towards the bamboo and the top angled away from it - with the top of the barrier visible above the soil so that any rhizomes trying to hop over the top of it can be easily spotted and chopped off.
Your neighbour may also wish to ask the company what depth they recommend for his/her particular bamboo – as it may possibly only need installing to a depth of about 18 inches.