For bleeding, I recommend washing the finished quilt in the largest front-loader at your local laundromat, using Synthrapol as your detergent. You want a machine that uses as much water as possible so that any dye bleed becomes highly diluted. You also want a detergent, such as Synthrapol, that suspends dye particles in the water so they don't settle into other fabrics.
You mentioned washing the blue fabric with the background fabric. Did the background fabric absorb any of the blue dye bleed? Some fabrics are resistant to dye bleeds and not affected by them.