I was wondering the same thing a while ago, and I dont remember the site but I saw on the internet that it was toxic for cats, so I did not take any chances.
Bamboo is basically in the grass family from what I've been told, so I'd be surprised if there weren't some types that are edible. However, I haven't come across any specifics.
Good subject... I think shredded bamboo shoots, well known in asian cuisine, are very chewy but not sure if the chewy texture is the fiber itself. Since it's edible to us, do you think they are also edible for tortoises?