Bamboo comes in two kinds, running & clumping. Running spreads underground by rhizomes.
Vegatative propagation, or establishing a new plant using cuttings from a donor plant and forcing it to root can only be done with tropical clumpers, not runners so you need to decide what kind you have to decide what technique will work.
The runners roots will grow at the node, the thick junction between segments, on some varieties. Take the whole culm (stalk), with roots, and bury it length-wise in the ground. Shoots will appear at the nodes.
Alternately you can layer them with the roots left in their original spot. Either a whole culm or only the branch bearing part of it is bent down to the ground and into a shallow trench, fastened in place by means of hooked or crossed stakes, and covering it with suitable propagating medium.
Clumping type of bamboos culm segments can be rooted. Take a piece of 2-3 nodes bearing healthy buds or branches. The side branches on each culm segment are generally pruned to a length of less than 10 in and the foliage removed. Rooting hormone placed in the culm cavity will help. Cuttings are set upright or at an angle, with at least one node well covered. Cover the pot with plastic tented up from the culm. This keeps the humidity constant. Water to keep the soil moist and to let fresh air into the tent.
Digging up & dividing a bamboo is best done in early spring before growth produces new shoots or wait for the growth period to be over late in the autumn. Never try to move it once shooting has begun.
A bamboo has two underground portions the rhizome and the root. You need to have some of both attached to the culm to sucessfully move it. Bamboo rhizomes are tough but must not be allowed to dry. Cutting can be done with an ax or I like a sawz-all, just use a clean blade or wipe it with 10% bleach before use.
Choose a clump with at least one cane that is more than a year old, ideally 2 or more culms. In general, the larger the division, the faster it will establish itself in the new location.
Take a 12" root ball for single culm clumps, and up to 18 - 24” for 2-3 culms. This will also depend on the size of the bamboo (height and diameter of the culms).
I usually cut part of the top off to reduce foliage and, therefore, evaporative water loss.
Good luck with your project