Bamboo is terribly difficult to get rid of as the roots are like iron bars in the soil - totally impossible to dig out without a JCB.

I managed to more-or-less kill some with Roundup. It certainly weakened it. Then it flowered and I thought "Great, NOW it's going to die!" but it hung on looking rather sickly for several years. Eventually the top growth did all die off (and I moved house) but collected the dead canes with permission from the new owner. As I was taking out the dead bits I saw that about 5% of the canes came out with new shoots at the bottom.
It's a "Terminator" of a plant.

I'd try Roundup when it starts growing in the spring - and probably again a couple of times during the summer. And dispose of the roots carefully - bonfires of bamboo are exciting as the sections of the cane go off like firecrackers.

I had the same problem. Some years back a "friend" gave me some dwarf bamboo. I planted it in a border and it spread like Billy Ho. I used a systemic weed killer on it every couple of months. It took two years to kill it off. I still have the stalks sticking up like straw in my border. Tried to pull them up.... Impossible. I'll have to dig them up soon as I want to use the area for something else.

you could get the bamboo membrane and dig a troff excuse the spelling round the whole plant . bury it slightly leaning outwards and leave half an inch above the ground . fill the soil back in and it will be kept within those bounderies . as already said its a night mare to get rid of . our local garden centre has stopped selling it which is an ominas sighn of the future . i think its going to become a real pest as time goes on .i have 3 types . two are in large nylon buckets with the bottem cut out and one has the membrane . the buckets are buried bye the way . they have all been stopped in there tracks and look lovley .