From my experience dyeing protein fibers such as wool, I know that to simmer wool in an alkaline bath will remove dye. Cotton, however, is a cellulose fiber and needs a different agent. A quick search online suggested peroxide may work for you. I don't know if you would have to simmer the fabric in water with peroxide, but I would think that may be the preferred method, as heat may be required. You may want to do a search online for how to remove dye from cellulose fibers. There were several chemical agents suggested in my search, but it seems like peroxide would be the safest.