^^ No, I just watched TDK the other night. Joker doesn't say Batman has been around for only a year. He actually says that a year ago the mob thought they were untouchable or something to that effect. Remember, too, that all those escaped Arkham inmates also had to be rounded up after BB. Batman might not have been able to devote all his attentions to the mob.
It is strongly implied to be some time around year. Joker couldn't have been running around much longer than that after the end of BB before he caught Batman's attention.
Also realistically, Bruce can't be Batman too long. Doing all that takes it's toll on the human body. It might work in the comics, but not in real life. Remember that Nolan was going for the realistic angle with these movies.