I'm thinking Bruce was officially Batman for about a total of a year and then some. Because in TDK, it takes place about a 9 months after BB, and I know that because in the movie, Joker makes a comment to the Mob saying, "Let's wind the clocks back a year, before Batman. These cops and lawyers wouldn't dare cross you. I mean, what happened? Did ya balls drop off." And the few moments when Bruce was Batman in BB was about a month. And the events of TDK is about 2 and a half months at least. And when Bruce returns as the Batman in the beginning of TDKR, it was about a month before he was taken by Bane. So all that together, Bruce was officially Batman for a year, a month and a half.