Honestly that sounds like an issue of the specific environment. Dust covers can only do so much. If the space is exceptionally dusty or musty, DampRid and a fan with an air filter are going to help more.

How dusty are these clothes getting between wearings? or are they things not being worn?

I'm familiar with musty smells, they originate in high humidity or water exposure, but dust itself I never thought of as having a smell? maybe I'm odd?