The difference between bleached and unbleached quilt batting, is essentially that the unbleached quilt battling is natural and the bleached is altered by man.
One of the purposes of bleaching quilt batting is that makes the quilt batting stronger, and therefore more resilient than unbleached quilt batting. Many people believe that bleached quilt batting is easier to handle than unbleached quilt batting. Therefore, many people will bleach the quilt batting before carrying out can craft techniques.
If your quilt has a white top, then this will be enhanced by bleached quilt batting. However, if the batting is not bleached, then it can make the quilt look an off-white color.