It's pretty impossible to even attempt to tally a single "canonical" accounting of Batman's years, since there are so many thousands of stories and no firm single "official" list of what is or isn't canonical. Plus, every decade or two there is some big company-wide event to rearrange the timeline and canon etc, due to the problem of characters not aging normally in serial endless storytelling.
The best official word is that, as of right now after the revamp/restablishment of the DCU with the New 52, Batman is about 35 years old, and has been active for supposedly a decade. However, if you took the stories that are assumed by most readers to be canonical, it surely adds up to far more than a decade, and probably in fact something closer to a couple of decades or more. This is complicated and confused due to some history being relegated to other dimensions, some vagueness about what is or isn't canonical, etc, and by the fact Damian Wayne -- Batman's son by Talia al Ghul, daughter of Ra's al Ghul -- is evidence that all of Batman's long history with Ra's, during a time when Batman was already the world's greatest detective, took place several years ago and makes it hard to imagine he was relatively new as a superhero when all of that transpired.
I'd say that if we restrict ourselves to only the stories we know for sure are canonical, and guestimate as best we can, it seems Batman's core most important stories should take up a good 20-25 years or so of time, if we really give him the benefit of the doubt and crunch the time as tightly as possible with little unaccounted for days at all. This leaves out a huge amount of stories and time, obviously, so adding in a lot of the other necessary elements, we'd probably push it to around 30-40 years.
Batman's existed about 73 years, and was perhaps 25 when he started out, which would make him 98 years old total if we counted literally from day one. But remember, the books come out monthly, and some events are assumed to overlap others (stories that transpire over longer periods of time give unaccounted space that is filled by other stories, for example), and so you could argue it's closer to only 45 or so years of history atop his 25 year old starting age, for about 70 years. Regardless, it's probably not entirely beyond the limits of a human lifespan, but it definitely seems to push it, if you account for all of his adventures.
More questions on Batman:
- I want to start reading Batman comic books, where should I start?
- What made Heath Ledger's portrayal of The Joker legendary?
- Why does Batman save the Joker from falling off to his death in the Dark Knight but let Two Face fall? Doesn't he kill Two Face by doing this?