Here's an actual photo of Bat Masterson (standing) with Wyatt Earp.
I did an image search for Bat Masterson as portrayed in motion pictures, and couldn't find a single one which showed him with a mustache.
I did find this, however:
That's the actor Zachary Scott (1914-1964), who was in fact a distant cousin of Bat Masterson. The context was ambiguous, and i don't know if they were implying that he had played Masterson in a motion picture, or were simply noting that he was related.
Can you link us to the quiz you are taking?