I read somewhere that it is not a good idea to dry-clean quilts but can't for the life of me remember why.
One thing I might do is get a couple of q-tips, dip them in hot soapy water) and rub over a colored piece. If the q-tip discolors, you know the fabric will run.
I'm sure others will weigh in with washing options from a loose rinse in the tub, to adding color catchers and/or using Reatayne and Synthropol. These products are meant for setting dies or catching released dies. I'll be watching this too because I have a red-white-and-blue one ready to be washed.