Where I live it gets very humid. That may have helped keep down the dust with the peat moss.
Otherwise I’d probably have gotten out my garden sprinkler can and sprinkled the top of the bed. So long not too much liquid is put on the bed the dust sort of forms a crust.
The other “bad” things about peat moss of bedding are that it is also super good at absorbing the oils in the horse’s coat, there fore it is harder to get a shine on the horse, and the owner has to be vigilant to clean the horse’s hooves out a few times a day so the moisture in the horse’s hooves does not get all drawn out. I’d also let the outside watering spot overflow some so that the horse gets to stand in some mud periodically.