Bamboo furniture and objects that become soiled can be cleaned easily with water and salt.
Pour lukewarm water into a cleaning bucket.
Prepare a small dish of salt.
Find a non-abrasive scratching cloth. The plastic ones are ideal.
Sprinkle some of the salt on the stained area of the bamboo. Take the cloth and dip it in water. Squeeze dry.
Rub the cloth over the salt on the soiled area. Do this gently but repetitively. Continue until the stain lifts.
Try a stronger method if this approach does not work. Add 3 tsp / 15 ml of household ammonia with 3 tsp / 15 ml salt that has been dissolved in 1 quart / 1 liter (0.3 US gal) of water. Scrub as suggested above. Wipe off with clean water and leave to dry.
Polish as appropriate for bamboo.