Did you soak the yarn/fiber beforehand? I find a good soak in warm water with a glug of vinegar helps a lot. Also, it sounds like you need more heat/cook time. Do you have a crockpot? Toss it in on low heat for two hours, keep an eye on it, just in case you don't have enough water in it. Then, since you're having trouble getting the color to stay in, try letting it sit in the crock pot with the lid on until cool, or overnight. Then try to rinse it. I don't know if it'll help, but it's worth a shot.
Thanks!! I'm not sure what it was, but I tried both suggestions and.... success!!
Dyed soy silk that doesn't bleed:
..and here is that silk/alpaca blend I dyed on Friday, which is becoming a pair of convertible mittens. I have mixed feelings about the color combo--I think it's the Christmassy red and green that's putting me off: