You're washing cotton,
Most fabric has very little bleeding these days so I pre-test the darker colors by soaking a corner of the fabric for a few minutes in a clear bowl of very hot water. If after a few minutes the water is turned, I put it aside. If the bleeding is minor I just wash it with like colors and detergent. That usually works for minor bleeding.
Fabric that bleeds alot I treat seperately. I always use a little detergent.
peace :D