But if you don't wash you will have the problem of the dark blue bleeding? (If it's the same fabric as the backing, possibly even if it's not?) It sounds like you will need to try to eliminate the bleeding without shrinking, which means not putting in the dryer or using hot water. Can you experiment with just soaking in cold water and see if you can control the bleeding that way? You certainly don't want the dark blue to continue bleeding on the white.