You could always take the initiative to give the mats a good scrub with water and a little rubbing alcohol once in a while if it bothers you (I myself have been considering going to class really early one day and bringing a bottle of rubbing alcohol and a rag.) There isn't much you can do during training. I just make sure to thoroughly clean my feet, hands, and face when I shower after training. That's really all you can do.
Sarah, wondering what it would be like to train in a bubble. Hmm...