How do you actually get costumes in tiny tower?
Solution 1:
Menu -> Bitizens -> [Insert Bitizen name here] -> Dress Up -> Costumes -> [Insert Costume here]
Once you buy the costume it is available to every other Bitizen in your tower.
Solution 2:
There is a button that says Menu on the bottom left of your screen. Then click on the Bitizens icon (which is the first one). Next, you pick any bitizen that is living in your tower and choose dress-up. A large green button with the word costumes should be there.