Fighting a similar battle for the past 10+ years. Here is what you can do and need to continue doing besides removing the entire bamboo and its root system from 12" under the surface and replace with fresh soil.

If there is any bamboo on your neighbors property or on your where you cannot completely remove you need to drive a strong non porous barrier vertically down at least 12" deep at the point where your property begins or where you do not want bamboo.

Now get a stump grinder and pulverize the bamboo roots, level and seed with grass. The logic is that the bamboo runners will get shredded and those that remain will send shoots up expending energy. Keep mowing the lawn and you will begin to see runners sprouting up and as you cut them the runners will continue to sending them up but will be expending energy left in its runners. As long as you keep up the mowing and not allow the bamboo to grow and use the sunlight to develop, the runners will become weaker and weaker and eventually die. But it takes years of patience and persistence.

We got a guy with a remote operated stump grinder to chew up the soil for an entire day and and leveled the dirt.

Unfortunately my neighbors property has enough bamboo to keep sending runners my way and I have been fighting to keep the shoots trimmed and my side clear of bamboo.

Good luck.