Why was Birdman on limited release?

Simple: it's most likely a marketing strategy.

The two tactics employed are called either limited release, or platform release.

Limited release is when a movie is released to a limited number of theaters in an effort to gauge the appeal a film may have to a wider audience.

Platform release is when they release a film to see what kind of word of mouth it generates as well as marketing buzz, in addition to its per-theater gross. The movie earns good buzz with audiences and has a high per-theater gross? They'll look to gradually expand the number of theaters it's in. This tactic requires careful planning, though, as pushing the movie to too many theaters too soon could lower the per-theater gross of the film, which makes it appear weaker.

While I can't say for certain which of the two Birdman may be employing, the idea is that it's more of an artsy independent film, which usually don't see audiences rushing out to theaters to see. As such, they release the film in a limited format to gauge the interest of moviegoers before gradually opening it up to more and more theaters, and thus a wider audience.

Given its relatively well reviewed status, generally positive buzz, and decent per-theater gross, I'd expect the number of theaters it's available in to expand.

While it's scored highly among critics and fans alike, it's still an indie film. Indie films just don't have the distribution channels that major studios have.

If the film continues to do well and maintain favorable press, it will probably get re-released to theaters like the movie "Chef" did (most likely after an infusion of capital from firms who know there's a market for it based on reviews).