Bruce wayne is temporarily living in a penthouse in Chicago (I mean Gotham) and the penthouse has huge windows overlooking the city, with endless buildings around him. He chooses at one moment to sit in his batsuit, minus mask, facing 2 windows where any one of thousands of people in nearby buildings could decide to look out their window or use binoculars or a telescope and see Bruce Wayne in a Batman suit. Given that Bruce Wayne is such a “celebrity” (reaffirmed by the gossip stories shown in newspapers whenever he does something interesting), it’s pretty plausible to think that at any given moment there are eyes trained on his penthouse windows.
I’ve heard some fanatics try to explain this away (“there are no nearby buildings”, “the buildings are too far”, “maybe people would think he’s wearing Batman pajamas”) but then there’s this other dangling question: Clearly in every scene when he’s in his costume, he’s got black face makup all around his eyes. Where was that makeup if he had just plopped down in the chair to stare so meditatively out the window? His eyes should have looked like those of a raccoon when Alfred came around to bring him breakfast.