By far, the most common mushroom found in houseplants is Lepiota lutea, otherwise known as the yellow parasol mushroom or the flowerpot paraso. This mushroom grows year-round in potted houseplants, and bamboo, given its need for moist soil, is no exception. The mushrooms show no preference for any particular plant -- it's the soil they love and the organic matter in it.
The mushrooms likely developed from spores that landed in the soil from elsewhere or they were brought in with the potting mix. Mushrooms have a thread-like reproductive system called the mycelium. This system isn't visible, as it is very fine to begin with, and is also underneath the soil. The mushrooms themselves are the fruiting bodies of the mycelium that appear under the right conditions and expel spores to create more fungi.
According to Jade Mountain Nursery, based in Tacoma, Washington, bamboo plants prefer moist soils year round. In the winter, this can be difficult to achieve with the drying effects of indoor heating, but a light daily watering should do the trick. Try placing the pot on a pebble tray filled with water to increase humidity. In addition, remember that clay pots suck moisture from the soil so a plastic pot may be preferable, especially for the winter.
The mushrooms aren't really poisonous, definitely not to the plant, and not to humans or animals unless a very large quantity is consumed. If they don't bother you and you aren't worried about them being eaten, it's OK to leave them. If you'd rather not grow mushrooms and bamboo, pluck them out and throw them away and continue plucking them as they reappear. You might also consider repotting the bamboo and sterilizing the new soil by baking it in the oven at 180 degrees Fahrenheit for at least 30 minutes before placing it in a clean pot.