NakadaTo me he's kind of like a fascist because he tries to do everything himself, idk if that makes him left or right though
When it comes to his money, Wayne seems to be a benevolent oligarch who strongly supports social services for the poor and disadvantaged, but has no desire to overturn the political system or address systemic failings (apart from corruption and abuse of power, which he deals with on a case-by-case basis). As far as I can tell, he supports the continued existence of his multibillion-dollar mega-company, but also feels a duty to help people with his wealth.
So Wayne's treatment of his money is pretty clear-- he's a wealthy oligarch with a streak of liberalism. But Batman's political philosophy is a muddled one.
As a vigilante, he regularly circumvents certain aspects of due process. In The Dark Knight, there's a great scene where Dent and Wayne, at an awkward dinner together, discuss Batman's role as a vigilante. Dent compares Batman to the temporary dictators the Romans would appoint during times of military crisis. Dent, therefore, seems to believe that there are times when democracy should be suspended and power handed to a 'good' and somehow 'incorruptible' leader. Wayne, playing devil's advocate, then points out that you can't really trust anyone with that kind of power-- the democratic process should rule, and the government should always be strong enough to have the final say. Later in the film, Bruce-- talking to Rachel in one of the rare moments where he's 'playing' both Batman and Wayne-- says that he thinks Batman's time is over, and that society needs a hero who works from within the system: Dent.
So, let's get this straight: in his Batman persona, Bruce plays a law-breaking vigilante who feels comfortable 'suspending' the legal processes of democracy to do what's 'right.' As Wayne, however, he is completely aware of the problems this poses. When he's playing both his personalities at once-- with Alfred, or with Rachel-- he seems to acknowledge this paradox, and states several times that he's trying to help the system learn to fix itself-- to surrender the power he's assumed.
Ultimately, does Wayne/Batman trust government to do what's right, or does he think that individuals should be able to take more of the law into their own hands? He seems to acknowledge that both solutions have their uses, and ultimately hopes to create a world where the government can be trusted to fix its own failings. Though they don't fit easily into 'democrat' or 'republican' or 'liberal' or 'conservative,' these competing philosophies do touch upon modern political debates about the role government should have in people's lives.
I'd put him down, therefore, as a true pragmatic independent. This is probably why he's been such a popular character-- different aspects of his personality reflect different political philosophies at different times, and he manages to synthesize them into a single plan of action.