Batman lived. He never piloted the Bat out into the ocean, but probably ejected well before it ever left the edge of the city. The scene after the burial with Lucius Fox discovering that Bruce had done maintenance on the Bat was meant to show that the auto pilot had been repaired, giving Batman a way out of the apparently "final" ending with the bomb. Follow that up with John Blake receiving the package and instructions to find the Batcave as well as Alfred physically seeing Bruce Wayne alive at the end makes for a pretty unambiguous ending: Bruce survived. Suggestions that Alfred may have imagined Bruce and Selina in the cafe at the end don't really hold up considering the fact that Alfred never saw them together and only knew that Bruce was tracking her to get back his mother's stolen necklace. It would make more logical sense for Alfred to imagine seeing Bruce with Miranda Tate, or with an unknown woman. The fact that it was Selina and Bruce pretty much confirms that it was reality. I've also heard the suggestion that the lost necklace was brought up again during the final will and testament of Bruce Wayne scene because it suggests that Alfred used the tracking device inside the necklace to find Bruce and Selina.