Reds are notorious bleeders! I ALWAYS pre-wash them separately from anything else. First, though, I test a small strip in a glass of hot tap water. If a white paper towel turns pink, you know you've got a bleeder. I found a product online -- Rit Dye Setter, and it works great! I run new fabric through the serger so it won't ravel, then put it in a very large cooking pot on the stove with the prescribed amount of water and the dye setter solution. I start with the lightest colors, which makes it more economical(For the second piece of fabric, I usually add a teaspoon of the dye setter solution) then proceed to the next color level, etc. I've never had fabric bleed after using the above dye setter product. I have to order it online directly from Rit, because it's not carried in any of the stores here.
Jeanette