When Ulrich is being taught to dance, and Wat punches Chaucer for his remarks, he proceeds to stuff his bloody nose with cloth. However, through cutting from one view to another and back, you notice that the cloth moves from one nostril to the other, and back.
Maybe both nostrils were bleeding but he had only one cloth. Remember in the begining Will and the other guy share nose plugs,(*gross*)so it's not really too big of a stretch that he'd only have one cloth.