Hang your wedding dress out in the sun to air for three to five hours. The combination of the heat and the breeze should remove some of the musty odor.
Fill a large sink or a bathtub with enough lukewarm water to cover your dress. Add 1/2 to 1 cup of white vinegar and leave it to soak for an hour, before draining out the water and rinsing the dress.
Repeat, but use 1 cup of baking soda in place of the white vinegar.
Wash the dress by hand with the laundry detergent, according to the package instructions. This will remove the last of the musty smell, as well as giving it a light detergent fragrance.
Put the wedding dress back out in the sun until it's completely dry.