Because he's a superhero in a comic book. I know that sounds like a cop out, but I have different expectations for my superheroes than I do real people. I would not tolerate a self appointed vigilante like Bats in the real world, but I accept certain genre conventions when I'm reading my funnybooks. One of those conventions is that individuals like Bruce who work outside of the law are typically hyper competent and generally good people, even when exhibiting human failings. That is why they are acceptable in comic land. We (general 'we') also accept that Batman WILL be judging criminals and other individuals alike, it's the same leeway we give Wonder Woman, Superman and the rest of their ilk when they lay down moral judgment on those they deem 'wrongdoers.'
Besides, we can't blame Bats for not dying in the line of duty like some police officers unfortunately do.