If the problem is excess dye in the fabric, Synthrapol added to the water will help. Although it is most effective in hot water (which you don't want to use with rayon), it still works somewhat in warm and cold water. If you don't have Synthrapol handy, Dawn dishwashing liquid has a similar action. You don't need a lot of it -- maybe a teaspoon to a couple of gallons of water.
If the problem is that the dyes were never actually set, it's possible that nothing will help. Retayne can set dyes; however, it is usually used in hot water and it is recommended for cottons, not synthetic fabrics.
What you describe is crocking (transfer of dye when fabric is dry). This is usually caused by excess dye in the fabric that did not get rinsed away. I would try the Synthrapol or Dawn. Maybe soak for half a day, periodically agitating, then rinse it all out. If there is any color in the wash water, repeat the process. It can take several times to get all the excess dye out. If the fabrics never stop bleeding, your last resort is Retayne. If that doesn't work, nothing will.