Diane,
I have had a few red fabrics bleed no matter how many times I washed them.
I had a bad experience with a deep purple fabric bleeding into an important quilt after it was quilted.
Have you heard about Retayne? If I have a red or dark fabric that keeps bleeding after pre-washing, I treat it with Retayne. That works for me. I make sure it is very well rinsed - no soap or detergent in it. Then I soak the fabric in a solution of very, very hot water and Retayne, and then just leave it soaking in the very hot water until the water cools. Then test. It has worked for me so far.
You have to use Retayne before the fabric has been sewn into the block. Otherwise I guess you would "retayne" the bleed in the block also.
I have also read that repeated washing and soaking in a solution of Dawn Dishwashing Detergent takes bleed out of fabrics. You might try that with a block that is already sewn.
I would first serge the edges of the block to prevent it from fraying before subjecting it to a lot of washing
Judy