Violet Bandits run around carrying either 1-Up Mushrooms, 3-Up Moons or, rarely, 10-Up Stars. If they see you, they will start to flee. If you manage to catch them (which is easier if you have a Bandit Mask) and defeat them, they'll drop a Bandit Mask.
It's a Bandit! They run around carrying 1-Ups, 3-Ups or 10-Ups, but if they see you, they'll run! Killing one will get you a Bandit Mask.