[@FantasyChic] Basically what Lady A said. :) Dorothy was designed to be a sort of a hybrid of John Watson in BBC Sherlock and Bones from Star Trek. And given that she knows Gene doesn't have any formal medical training, she doesn't want anyone under foot. Too many cooks spoil the broth and whatnot. 

Edit: Oh, and Gene's first comment brought drama into the med bay, something Dorothy cannot stand while she's trying to save a life. She doesn't like it when people are in the med bay when she's working lol