I bought a new piece of red fabric, this time Kona Cotton. It still bled, but not as bad as the first piece I bought. I talked with a very helpful lady at Bear Paw Quilting in Coeur d' Alene and she recommended that I use a product called Synthrapol. It is a concentrated surfactant that a lot of people use for hand dyed fabric. It was $2.99 for a 4 oz. bottle, but you only use 1 teaspoon per gallon of water, so now I have something on hand that will take care of any future bleeding problems. Anyway, it worked like a charm--no more bleeding. I even used it on the first piece of red that I bought (the one that isn't as red as it used to be from so many washings) and no more bleeding from it either.
Now I can start on the quilt for my great-nephew!