Earth Friendly Yarns sells something called "Spun Bamboo", a brand name yarn, but it doesn't appear to be specifically organic.
Bamboo is generally considered a sustainable or earth-friendly fiber. According to Nature Moms,
Bamboo is the fastest growing plant on this planet. While some think of it as a tree it is actually grass and it grows one third faster than the fastest growing tree; it reaches a harvestable size in three to five years. Some species grow as much as four feet a day. It requires no pesticides, is harvested with no impact to the environment, and is capable of complete regeneration without need to replant. Bamboo also helps mitigate water pollution due to its high nitrogen consumption. This is great news for those conscious of the environment.