Make a solution of 1/2 cup bleach, 1 gallon water and a sprinkle of laundry detergent. Soak the swimming suit in it for at least 10 minutes. Wear latex gloves and use your hands to swish it around and wring it out.
Use a solution of 1 cup vinegar, 1 gallon water and a sprinkle of laundry detergent instead if you are concerned about using chlorine on the material. Again, allow it to soak for at least 10 minutes and swish it around and wring it out.
Wash the swimming suit as you normally would in the laundry. If you find the odor to be very unpleasant you can soak them in plain water before washing to dissipate the vinegar and bleach.