I can tell you exactly what will happen if you do this because I have done it. I was testing an out door shower at Burning Man two years ago. They were setting up a group water fall shower... and it was a very cool set up; however, they had also just added the chlorine (bleach). They didn't add much. Just enough to make sure the water was debugged. I stepped in and took a shower. No problem. Felt fine. I stepped out and started to dry off. While I was drying off... my skin started to crack and peel while I was toweling... that fast.
Bleach will blanch you skin. It is caustic. DO NOT DO THIS.