The sustainability of fiber farming Cotton, Bamboo, and Hemp all depend heavily on the cultivation methods being used. That being said we can compare the function stacking ability of these crops.
Organic Cotton is an perennial plant that is grown as an annual crop so requires effort and Energy every year to get the crop started. It also require a great deal of effort in managing it during the growth cycle since you need to limit vegetative growth to get a good yield of cotton. It is grown specifically for the fiber found in the cotton flower while the rest of the plant goes unused with the exception of the seeds which get pressed for cottonseed oil. I am unsure of guild relationships with the cotton plant, but generally it is grown in a mono-culture so that is of little concern here. The fact that it is, for the most part, grown in mono-culture with "conventional" (even if it is organic) agriculture means that the soil is not being cared for properly which is a really bad thing.
Bamboo is a perennial grass! It forms a thick matted root layer that suppresses growth of other plants, so it doesn't have plant guild dynamics, but acts as a great way to suppress the spread of plants from one place to another. Bamboo also has several other uses other than harvesting for fiber. It is grown as a windbreak or hedge / living fence. The young shoots are human edible, or used for forage. Older stalks can also be used as goat & sheep forage, so you can obtain, wool, leather, milk, & meat from a mixed production bamboo forage system as well as bamboo fiber! Of note: due to the very high water holding capacity of bamboo textiles they will take more energy to dry than cotton will. If you use a cloths line instead of a dryer then this isn't an issue.
Hemp is an annual crop that grows invasively like a weed so there should be very little environmental concerns with organic mono-cultures as long as a cover crop gets planted from late fall to early spring. Read this article to see which companion plants are great to grow alongside hemp to reduce pest issues. Additionally Hemp can be grown as a companion plant to potatoes to help fend off late blight. Hemp yields a large quantity of seed, which is considered a superfood. I have heard of hemp being used as an amendment to cattle feed, so I am sure other animals would do well with it as well. Hemp also has found use as a source of graphene for technological applications. The hemp fibers are also useful for making Hempcrete which allows for buildings that sequester carbon.
Work is currently being done to use bamboo fiber in a similar way with Magnesium Oxide cement instead of a lime based cement like portland cement, but Hempcrete is a far more established technology.
Also, as THelper recommended in a comment on your question, have a look at this question.