With batiks, I run them under water and then squeeze them to see if they are going to run. If they do, I continue to do that until they stop running, THEN I wash them. Even if they don't run, I'd still wash them.
I would also wash the white (separately of course).
Then I'd use a colour catcher when you wash the finished quilt.
(Can you tell I've had a problem with this before?)
Watson