My back wouldn't take washing a quilt in a bathtub. It works just as well to use a top-loading washer; just do not allow any agitation. Fill washer with water and soap, stop machine, add quilt, agitate by hand pushing down on the quilt, advance switch to spin, spin out wash water, fill with rinse water, stop machine, agitate by hand, advance switch to spin, and spin out rinse water.
Aside from being easier on the back, this method has the advantage of getting more water out of the quilt before handling. Water is very heavy and puts a lot of stress on stitching and seams.
Instead of hanging on clotheslines, where water weight adds to stress, I advocate laying out in the shade on top of a sheet, covering with another sheet (to protect against errant bird droppings), and anchoring with rocks.