Usually when a Bitzen is in the elevator, it has an exclamation mark notification with a floor they want to be dropped off on. But I have noticed some of them joining with a '?' and then they tell you which floor they want to be dropped off on after you click on the elevator.
Why the question mark notification?
Best Answer
Just had one in my elevator and taking it wanted to go to floor -2 which was my second Imperial level. Not only did it give me coins, per usual, it also shaves a minute off any work being done on that level. For example, I was creating Security Codes and had 7 minutes left. After dropping the bitizen off there, a little -1 clock marker hops up on the top right of that level and reduces the time.
Also referenced and somewhat confirmed other people noticing this here: http://quickgamer.net/games/tiny-death-star/walkthrough/
Edit: Just confirmed again sending a ? mark bitizen reduces production on whatever floor it wants to go to by 1 minute.
Edit #2: Also verified that you can send it to any floor to get the time reduced even if it's not the one that it wants to go to. You won't get coins, but it still reduces the time by 1 minute.
Edit #3: Also side note, you can send any bitizen to an imperial floor to reduce the time by 1 minute at any point in the game.