I've seen this problem when using a low quality detergent (bulk or no name brand) combined with large laundry loads. What happens is that the detergent does not fully dissolve and the large load causes the frothy detergent to splash around the upper parts of the laundry machine where the rinse cycle does not normally cleanse. Over time, the detergent collects in the upper parts and remain damp for extended periods. This is a great place for mold/mildew to eventually grow and give you a sticky moldy towel smell. Now every new laundry load cycles some of this mildew into your clothes and give you a nice clean smell ... NOT! This explains why your bleach loads comes out okay. The bleach kills the mold/mildew.