I think you're thinking about the problem from the wrong angle. There's three parties involved here - the filmgoer, the film maker, and the venue owner.

If you ask yourself "are there indie film makers absolutely desperate to find places willing to show their films", and "are there bar owners absolutely desperate to find ways of increasing their trade on a quiet Tuesday night", then I'm guessing the answer is "Absolutely".

And I'm also guessing that if somebody can do both services effectively enough, the two parties would happily pay a fair amount for that service.

I'm currently reading David Byrne's "How Music Works" and he's quite clearly talking about the need/opportunity for startups to plug the distribution gap for low volume indie musicians, and I don't see that the indie movie world is a great deal different to that.