You could try putting a couple of drops of bleach in the lid of the Clorox bottle. Then add a few drops of water. Apply this around the outside of the stained area (not too close!) very carefully with a Q tip. Then wash as usual. This works for small spots assuming you don't mind a bit of fading. I have only used it on white tablecloths. It also gets out food stains.
I usually soak all red floss in a mix of vinegar and water before using. Seems to work to set the color.
Good luck.