Pretty sure they didn't have the coded lock on the armory at the time. They had keys that only a few people in theory had access to and they forgot Bill would have one of those keys. Remember that's how Datu and Burt figured out Bill was able to steal the stuff? Burt figured Bill would have access to the keys to the building, and Datu then realized about the elevator.
So Bill stealing things was as simple as walking downstairs and turning a key.