Your plant is a type of Dracaena, specifically Dracaena sanderana, and not a true bamboo.They need good light, but shaded from sunlight. Too much sunlight will burn the plant; not enough light will cause poor growth and stretching and poor color. It's best to remove some of the bottom leaves so the plant can concentrate on growing the stalk.

Dracaena do not like fluoride in their water which causes browning. Make sure the roots are covered with water; add water to keep the water level constant. Every couple of weeks change the water completely. Refill the container with clean water. Lucky bamboo is sensitive to the salts and chemicals in tap water; use distilled water or rainwater if possible.

You can use a water soluble plant fertilize diluted at 1/4 strength once a month. Do not over fertilize which could burn the plant. Your lucky bamboo is usually grown in a couple inches of water and gravel.

Sometimes yellowing will occur on the plant.  Stalks can turn yellow from bottom up, caused by too much fertilizer. If this is the case, replace with distilled water and don’t fertilize. But sometimes when the stalks turn yellow it is too late for the lucky bamboo to recover. It is often better to cut the green top off and start a new plant. If you have more than one stalk in a container, but only one is yellow, remove the yellow stalk and change the water.

You may decide to take cuttings of your plant as well. You can do that in spring or late summer. If older pieces of stem are used, they should be cut into 1 1/2 to 2 inch pieces, each of which must carry at least one growth bud (node, a slight swelling noticeable under the soft bark of the stem) and place in water.

Courtesy of the NYBG Plant Information Service