Sounds like your bleach is too strong, you need to dilute the bleach with water. Try 50/50 water/bleach. Don't leave it in very long, pull it out every few minutes..rinse it off and dry it and look at it under the light. Keep doing this... checking the progress until you get the result you want.
I usually have the opposite problem, I guess my bleach is too "vintage" Bleach seems to get weaker when it's on the shelf in the laundry room for years on end.