Keep rinsing in cold water until it runs clear. What is going down the drain is simply residual dye that didn't get absorbed. After you've rinsed it clear and dried it, a couple-three washings will take care of any bleeding later on. This is why dying to a darker shade is recommended, to ensure that after washing etc. the desired shade is acheived.
Yes, adding salt during the dying process helps alot.
I also use a couple tablespoons of white vinegar as well sometimes. It depends on the material being dyed.
