Once they are repaired, it's easier to wash them in a top-loading machine than in the bathtub. Just do not let the machine agitate.
Basically you fill with cold water, add a gentle soap (there are special ones available for quilts), stop the machine, add the quilt, hand agitate by gently pushing down on the quilt, turn the machine to "spin" to get rid of the wash water, fill with rinse water, stop the machine, hand agitate again, advance the machine to "spin" to get rid of the rinse water, rinse again, etc. Using the machine is *much* easier on my back than washing in a bathtub. It can also be easier on the quilt because more of the water weight is gone before you lift the quilt; water weight places additional strain on seams and can break stitches.
Do not machine dry. The best way to dry is outside, in the shade. (Avoid sunlight; light fades fabric!) Lay a large flat sheet in the shade, lay the quilt on top (gently squaring the edges as necessary), lay another large flat sheet on top of the quilt (to further protect against sunlight and also against bird droppings), and anchor the edges so nothing blows away. You may need to turn the quilt over once to thoroughly dry.