Summarize:

Often times natural food, and plant-based oils have a wonderful aroma. They also have the added benefit of moisturizing your skin. Since bleach dries out the skin, it is a win-win: no more dry skin, no more chlorine stink. Some suggestions include:  Coconut oil Almond Oil Olive oil Aloe Vera lotion: make sure the lotion is high in Aloe Vera as that will make a huge difference in its effectiveness Tea tree oil lotion: like Aloe Vera, a higher concentrate will do a better job Citrus based lotions Citrus based soaps: there are some all-natural soaps that provide both the cleaning power of soap and the moisturizing effects of lotion. Check your local health food store to see if they have any that fit your needs and budget. When using oils you don't want to overdo it. You could wind up over-oiling yourself, thus adding another step (namely, removing all that excess oil!). If you're using lotion, this should be enough to coat your entire hand and give you a good idea if you need more and if the lotion you've chosen is doing the job. If you use a citrus based soap, lather up then use hot water. This helps the soap latch onto those base bleach molecules and lift them out.
Use select natural oils, lotions, and soaps. Apply a little at a time. Apply a few dollops. Lather up.