If I buy a costume in Tiny Tower, will all of the bitizens be able to wear it

From personal experience, even if a bitizen moves in with a costume you haven't bought yet, it won't be unlocked for other bitizens unless you buy it with tower bux.

In addition to what Ashley Nunn has stated, I would like to add that it is now possible to select a specific floor to build (thanks to a recent update on iOS, that is. Unverified for Android users)

When you build a floor, where you would normally have to select "Retail/Food/Residential/Service/Recreation/Creative", they will now be labelled as "Random [type]".

Below this, there is an option to "Select Specific Floor", which will enable you to select the exact floor you want to build. It does, however, cost a fairly significant amount of Bux.