I wash my bike stuff in the regular hot water load, with whatever brand of hypoallergenic detergent I am using. I wash them on hot, as it seemed to stop the various infections I was getting. It's caused no problems. Jerseys get washed on cold.
Hang the shorts to dry inside out. My newer jerseys don't get put in the dryer, but I have a couple of Terry jerseys from 5-6 years ago that can go in the dryer.