i only dye silk, tho i have done work with cotton before, just silk is my venue, i think that looking into dhrama trading company which is based in california is an excellent source for information. i do not use natural dyes as they do not give me the vibrant colors i am after, different fibers require different mordants (setting agents), (ie acids for silk, i just use vinegar, it works, well and does not hurt the enviorment)with cottons some of the possibilities are
annato, sandlewood, indigo, cochineal (ground up bug, kinda icky i think), henna. onion skins, these are set with alum, cream of tartar, soda ash, or tara root.
one of the most important things i learned is that is it a protien fiber or a plant fiber, stains vs dye
as my scarf business is based more or less on silk, cannot give a lot of info, but i do use acid dyes (suitable for silk only) because of their properties and the fact, with practice (as in chemical cotton dyes) the dye is exhausted in the process, so nothing is left but clear water (do not drink, lol), i will send more resources if you wish, one thing to remember with natural dyes, is that you are unlikely to duplicate a color, and that is part of the charm, pm if you wish
jan in palatka
fabric_fancy also is familiar with the products and i suspect she is more knowledgable than i