It's not bamboo. You have a houseplant that is marketed as Lucky Bamboo, but is really Dracaena senderiana. There is a separate, Lucky Bamboo forum at GardenWeb for folks who have this plant.

Brian- My potted bamboo have very little rhizome showing aboveground, and they have a pretty decent belowground root mass if they have been in the pot for 6-12 months. When I'm doing divisions of bamboo from in-ground groves, I tend to use a root pruning saw, a corded SawzAll if I'm anywhere near electicity, and a lopper, depending on what I encounter. Typically, I try to get through the rhizomes in the gentlest way I can because I think it induces less shock. I have used an axe, but don't find it very efficient and I don't like the results. I'm just getting into propagation from rhizomes because my bamboo are sending out a lot of nice runners in my new location.

I've held perennial plants in pots over winter many times. Just make sure you protect them from freezing and thawing temperatures constantly. That will harm the roots. Freezing OK, but up and down not good so the more it happens, the worse for the plant. I often cover mine with wood chips or leaf litter.

duplicate post : https://www.houzz.com/discussions/6054633/can-someone-please-give-me-tips-on-how-to-save-my-bamboo-palm#n=1 lol.. i thought you had 2 ... until i finally realized the mirror .. lol ... i was going to try to figure out if one was doing better than the other.. which might indicate a pot problem ... lol