Ask questions, meet dancers, and be part of the conversation.
Well, while I've never seen a pro refuse to take on a student just based on their personality, you'd be surprised how often pros will encourage students to move on to a different teacher or even flat-out dump them...
Does this have anything to do with your 2-instructor question? If the instructor knows you are already taking lessons with 2 other teachers, he may feel that he doesn't want to be a "third-wheel."