When I was in Bali recently I became very interested in the basket weaving. I would like to identify the Bamboo they were using but I only got as far as translating it. To the locals it was the bamboo you can tie a knot in.
If anybody can help me with this one I would appreciate it.

Because you encountered it in Bali and you were told you could tie knots with it, it is probably the following:

GIGANTOCHLOA apus: 20m x 15cm, APUS
Known as “PRING TALI” in Indonesia. 'Tali' means string which can be split from the young culms and has suppleness of leather. The most important construction species in Indonesia, strong and durable.

The bamboo below is the one commonly called weaver's bamboo:

BAMBUSA textilis: 12m x 5cm, -9°C WEAVER’S BAMBOO
A beautiful plant native to southern China with long internodes and lacking branches in lower half, a preferred species split for weaving crafts and utensils. Culms can contain Tabasheer which is used in Chinese medicine for febrile diseases, delirium and infantile epilepsy. Following varieties available:

Information copied from:

EARTHCARE ENTERPRISES - NURSERY CATALOGUE – 2011

In terms of weaving, can any of the Textilis be used in this way, eg, Glabra, Fusca or Gracilis?

I'm no expert but as far as I know all textilis (and probably all thin walled bamboos) can be used for weaving. One advantage I've noticed with textilis is that the splits are much less likely to cut you than those of some other bamboos - surely a big advantage when weaving.