You can cut an established plant/grove of bamboo off at ground level and it wil not kill the plant. It will grow back.

Your best attempt will be to dig up a culm, preferably a few culms, with a good sized rootball and transplant that.

How tall is your bamboo, or do you know what kind it is?

Kt

mandie-
Bamboo is not like most other plants, and cuttings generally don't work. (You can do this with a few tropical bamboo, but that's another story.) To get a viable new plant you will need to do some serious digging, prying, and chopping through the underground rhizomes until you can free a large rootball as intact as possible. Don't disturb the roots any more than necessary; immediately repot.

Mandie
By any chance is the bamboo you're growing the plant sometimes called "Lucky Bamboo"? Just wondered. Can you post a picture?
Bruce

What kudzu9 said. You have to split a lump off from the root ball with a fair few culms to ensure success rather than just one small piece. Don't worry this won't hurt it, they are tough! Make sure you water well once transplanted.

What species is it? Hope you manage it.

Chris
Take it or Leaf it

Hello,
The first question to ask is "Is your bamboo a running bamboo, or a clumping bamboo?" If its a runner (leptomorph), it's very difficult and most times impossible to propagate from the cane, unless you're growing from tissue culture.
If it's a clumping bambo, you might be in luck. There is only one clumping species of bamboo that I know of that could live in your zone. It's the Fargesia species and subspecies. I'm not sure of fargesia's culm propagation success rate is, but here's how I propagate mine.
I cut part of the culm with 2-3 nodes intact. I like to use culms with buds that have not branched yet. I bury them in pot in a slightly off kilter vertical position leaving one bud just sticking out of the soil. Put it in the shade, or keep it in the house this time of year until spring. In one pot I usually put five cuttings in because with some species you may only have a twenty percent success rate, so it's a good chance you'll get at least one plant per pot.
Also, any soil including sand will work, but the most important thing is that you not let the plants roots dry out for even one day. After a couple few months, you should have some leaves. You can then slowly introduce direct sunlight. Just shade the pot, but not the plant, because a potted plant does not have the same advantage of plants in the ground of staying cool.
Now, having said all that, I sure hope your not talking about lucky bamboo.
Here's a pic of the bamboo that I propagate from the culm and roots, and branches through air layering. These matured to five inches thick.