Probably the laundromat is your best choice as others have suggested. I would not use any soap, just some liquid fabric softener, which is a gentle cleaner in inself and maybe even 3 or 4 color catchers. They can be reused so you are not wasting them. Use only cold water and really all you need is a good rinse ... not the whole cycle. If you use the dryers, make sure the temperature is as low as possible and keep shaking the quilt out every quarter or so. Or just dry a little bit, take home and use the sheet underneath in a shady yard idea.
Good luck!