Your reference to "stalks circularly wrapped around the rim" is quite a common thing. It's actually the root system, not a culm (stalk). It happens when a bamboo has been in a pot long enough to send out roots, and they start to circle the pot when they can't get out. With tropical bamboo you can propagate from the culms, but with the temperate bamboo you are growing this won't work. What you can do is give them adequate water and some fertilizer, and then dig divisions when the bamboo runs and sends up new shoots (but don't do divisions until late fall or early spring).

To keep my runners under control, I rhizome prune with a sharp shovel, and I have occasionally succeeded in getting new plants by taking pieces of established, underground bamboo rhizome and potting them up in large pots. My success rate has varied from 0-50%. It's highly dependent on getting a good piece of mature rhizome (with lots of small roots), and on the species.