I would just throw it in my washer on a gentle cycle with warm water and a mild soap or detergent. Then machine dry but don't overdry.
I use orvus to do all of my laundry. I buy it from our local farm store by the gallon jug.
I have never had a quilt fall apart on me. I also washed my daughter's wedding gown the same way after she drug the bottom and train through the muddy grass at the outdoor reception. I didn't put in in the dryer because of the trim but it came out beautifully.
I know that many quilters recommend the bathtub routine. I personally am not strong enough to wrestle with a soaking wet quilt. And forget kneeling on the floor in the process. Since it is physically impossible to wring as much water out of the quilt by hand as it is in the machine I am afraid hanging it up would be harder on the fabric than the dryer.
Since it is not an antique do whatever works for you.