Are your sure its "dust" as in dirt? It could be wax from the hay stems that's not been removed by a conditioning process. (That's one thing a conditioner system helps with). Could also be mower teeth, mower reel tines, rake and or baler pickup tines hitting the ground. Clover is a high "dust" wax content plant (alfalfa of course, too). Have a lot of ant hills or moles or woodchucks in you fields?
Applying carboxylic acid ("propionic acid") is usually acceptable to cow outfits, but around here horse people generally don't want it in their hay. Their horses are often too picky and won't feed on it. Try a sample yourself. How about a too much battery acid in your salad. Once your hay has this black mark in the neighborhood, it will be hard to convince buyers to come back to you.
Take a look in your baler in the knotter area and have the "dust/dirt" analyzed. See if it dissolves in water for example. If its dirt, raise your cutter bar and pickup teeth. If its wax, rake it more aggressively. This can spin off the wax more thoroughly. (as well as the nourishment value)...
