I realize this is a really old thread, but I'll post my experience here anyway in hopes it might help someone else in the future.
I washed an unquilted top once because I discovered one of the fabrics was going to bleed, but I did it very carefully and was successful. Here's how I did it:
I filled my top-loading washer with hot water, added a tablespoon of Dawn, put the top in. After the machine was done filling but before it could start agitating, I pulled the plug and let it sit overnight (12 hours). The next day I plugged the machine back in, hit the cancel button, then set it on a rinse-and-spin cycle. The quilt top was never agitated. It drained and spun "dry" (damp). I laid it out on my living room floor to air dry. The bleed was permanently fixed, the back of the top had no stringy nests or mess, I was a happy quilter!
p.s. LOVE my Speed Queen.