I have two candidates I've always felt that Terri Mcginnis is the rightful successor to Bruce as Batman because he was trained to be Batman. Many were trained as Robins but not one specifically. Also in JLU it was revealed he was also Bruce's son. That being said I also feel Damian Wayne is another rightful successor as he's also Bruce's son and was also trained by Ra's al Ghul himself. The other's Tim, Jason, even Dick they aren't really successors their protégé's and quite frankly I feel that Jason(until he became Red Hood) and Tim served to just be Robin. Dick on the other hand I'm in a gray area with him he's the first Robin logically he should succeed Bruce but he once said if I'm not mistaken "I'm not Robin and I'm to optimistic to be Batman." His personality just isn't dark and broody enough same with Tim. Also Jason is too much of a stone cold killer to be Batman.
Ultimately I do feely Terry is the rightful heir to the Batman mantle because he was trained for that express purpose.