He's clearly a man with a mission, but it's not one of vengeance. Bruce is not after personal revenge... He's much bigger than that; he's much more noble than that. He wants the world to be a better place, where a young Bruce Wayne would not be a victim... In a way, he's out to make himself unnecessary. Batman is a hero who wishes he didn't have to exist.
About Batman's motives, as quoted by David Mazzuccheli in his Afterword to Batman: Year One.