I've finally dug out the last lump of the bamboo clump, but still have to trace about half a dozen runners and get them. The bamboo itself didn't root too deep, only a matter of 6 inches or so. The bigger problem was the roots of the buddleia and Rose of Sharon which were growing amongst the bamboo.
On the positive side I have about 50 canes now ranging from 4 to 13 feet in length, gave probably the same number to my neighbours and still donated about 100 to a local gardening club. Yup, it was quite a stand of bamboo.
I'd always disagreed with those who said that bamboo is invasive, and I genuinely never had a problem until a couple of years ago when I had work done in the garden. The people doing the work removed the timber I had buried in the soil to contain the bamboo and the bamboo went for freedom very quickly after that.