In place of bleach how about Borax? It whitens the whites and I think it makes the entire laundry cleaner.
It is a natural product--when you read on the side of the box it tells what it really is. They mine it out of Death Valley and is a very old product. My Mom used it in her laundry.
You an also use in the kitchen, bathroom counters ect, ect.
I love it!
Mariah