Reasonably, Batman does not go out on patrol every single night, all night long. It's pretty unbelievable. However, he may go out most nights and he almost definitely has a completely inverted sleeping schedule. He most likely sleeps during the day and goes to work as a hero at night.
That being said, there must be times when Bruce Wayne must go out during the day.
As a playboy he can probably get away with mostly being seen at evening events but as the owner of a multi-billion dollar corporation there must be times when even the irresponsible and uninterested Bruce can't get out of a lunch or breakfast meeting.
Therefore, Batman must often but perhaps not regularly, go entire days without sleep.
This is my next experiment for Building Batman. I propose to remain awake and functional for 48 straight. It's probably pretty rare that Batman goes longer than that. An argument that he doesn't may be that he keeps his physical self in peak condition and therefore must see the value in self maintenance. That doesn't mean he sleeps long though in a crisis situation.
So here's what I think is reasonable. I'll get 4 hours of sleep between Tuesday and Wednesday (that's tonight). 4 hours between Wednesday and Thursday. I won't sleep at all Thursday night. Some friends of mine are planning to go out Friday and so I will go with them. I won't leave until the group disperses. After that I will allow myself to sleep as long as necessary.
I don't think this is very extreme and is definitely within reach.