Dracula was the first vampire (Dracula - Wikipedia, the free encyclopedia) but I do not see how this fact can help in answering your question.
To me, the conversation (context) you provided sounds like some sort of conversation between two airline employees serving, possibly, as cabin attendants. In that case "getting a Dracula" might refer to the hours they have been assigned to work. But, I am not at all certain about that. Maybe you could provide more context? What was the whole conversation - do you know?
Student or Learner