Acid dyes will not work on cotton or any other cellulose (plant) fiber.
Cyndi, I have to differ in opinion with you. I have dyed protein/cellulose blends with acid dye and the acid dye has always washed out of the cellulose fibers fairly easily. The cellulose dye in RIT is a direct dye and doesn't stay as firmly fixed as fiber reactive dye does. I haven't dyed any of my cellulose yarns with RIT (I have used it with wool and it worked fine IMHO) only because I learned my lesson before with cotton fabric.
If the garment is intended to be hand washed in warm water instead of thrown into the washer then the yarn might not bleed as much, but I'd still reccomend fiber reactive for cellulose fibers because it's just better dye and on the same price level, if not even a little cheaper.