Bamboo!!!!!

Hi Rowan,
Bamboo can be extremely invasive. You might wish to consider digging up as much as you can in an attempt to stop its spread.The roots will have spread and will cover quite a large area, so try to remove as much root as you can together with the top growth. I would not advise using any chemicals to try to kill it off at this stage, as you state already, as you might kill off other plants in your garden that you want to keep. Also, the chemicals will stay in the soil for some time. It will be really hard work, but if you can rally the support of some friends do try to remove it manually first. Also, try to contain it in future by planting it it a large plastic dustbin that has drainage holes drilled in the bottom. Good luck, and let us know how you progress.
Best wishes,
Grenville.

There are some forms that are much less invasive, if you want to try a different type somewhere in your garden when you've got rid of this highly invasive one. Welcome to GOY.
This is a very friendly site, even if you don't consider youself a keen gardener.

There are systemic weedkillers that you paint on the leaves of a plant and which are transported down to the rots and will kill off a plant without harning the soil. However with a very vigorous plant (such as your bamboo), this is going to take a lot of applications to have an effect.
I would suggest digging out as much as you can, as Grenville suggested, and treating any regrowth with the weedkiller until it finally gives up. Any good Garden Centre will be able to advise on the strongest but safe product to use.
Good luck,
Andrewr