I agree with Paul--try the clothes dryer first.

For washing, be sure to use a large front-loading washer, on gentle cycle. The agitator on a top-loading washer will tear your baffles. Trying to spin a sopping wet bag in a top-loading washer might also do serious things to your washer, too. Unless you have a large capacity front-loading washer and a large dryer, you might be better off to visit your local laundromat.

Excellent instructions on washing down sleeping bags on the Western Mountaineering site.