My primary RW comp suit gets so nasty I can't stand it, so yes, I wash it about three times a year. When your white suit turns brown and gray, then wash that rascal. I just stick mine right into the washer on regular cycle. I do not use the dryer; I just hang it up on a rack outside. I have never had gripper colors bleed onto the white, but they do fade.
According to Bev of Bev Suits....wash in cold water only, hang dry. Don't treat stains other than with the detergent you're using in the wash. Don't use anything with bleach in it. And beware of Tide and Woolite, they cause the colors to fade. Personally I use the color protector cheer. It has an ingredient to neutralize any chlorine in the tap water.