We had bamboo in our garden - it's fairly small, and there are two levels with a sloping bed and steps in between. The top level is about 3x5m - a row of running bamboo had been planted on each of the short sides by the developers (not us. We hated the stuff).
We decided to redo the whole back garden last year, and our amazing landscape gardener had to dig down until he could find no more roots, and then went painstakingly through the earth he'd dug out and pulled out all the runners. For some of it he could put the earth he'd dug into our skip, but as access is horrendous (through the house) it couldn't be done for all of it. Fortunately the running kind we had doesn't go too deep, so he didn't have to go down as far as a metre - probably about 40cm.
It was horrendous, it took him a week. The runners had gone everywhere on the top level and had started to go down the slope. We put in a bamboo barrier on the borders because it had escaped next door and we didn't want it back again. The bamboo barrier I bought was 50cm, and you leave 10-15cm above the ground as the runners break cover and try to leap over it. 
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However, it has worked. Not a single bit of bamboo has come through the barrier, or popped up in the new lawn, or the new steps to the lower level. We've not had to use any chemicals.
One thing to be careful of - some tips are not happy about having bamboo waste. Check before you drive in with a car full of the stuff. It wasn't a problem for us, but I've heard of issues elsewhere.