How old is Batman?

I was watching a video on youtube for the upcoming game, Injustice. In case you don't know its  DC comics based fighting game, made by the people who made Mortal Kombat. The video was detailing the author's hopes for characters from the "batman family". You see, over the course of Batman's career, he's had SEVERAL robins; 5 to be exact, 6 if you count Frank Miller's piece when Batman comes out of retirement..bla bla bla. The video got me thinking - how the heck old is Batman? I did some half-assed research (internet).

I am not an avid Batman reader. I know a good chunk of the main plot lines and a few tid bits from here and there, that's about it. To answer this little question I set forth and, more or less, pieced it together.

The easy part. Bruce Wayne became Batman at age 25 (I've also seen 26). The hard part - where to go from there. The easiest route was finding out how long he kept each Robin around. So, here we go, in order.

Dick Grayson (becomes Nightwing) was Robin for 9 years

Jason Todd (dies, comes back as Red Hood) 3 years

Tim Drake (Red Robin) 7 years

Stephanie Brown (became Batgirl) roughly a year  - she trained for several months and did a couple cases with the bat

Damien (at the moment he's dead) roughly a year - I'm guessing that because I could find much info on it.

As you can see...not exactly conclusive data, but enough to show something interesting. Based entirely on this, Bruce Wayne is roughly 46. 

This is saying that he had Robin from day 1 of being Batman AND there's no gaps between Robins. Chances are there was some time at the beginning without a Robin and some time between each, so I'm betting he's over 50. Pretty spry for an older gent!  From what I've read, Batman has fallen into a Lazarus pit, that Ra's Al Ghul, has a couple of times, making him younger, better, faster, stronger...sorry...Daft Punk tanget... Fun little waste of time