One more clue that proves that Batman is not dead is the final scene - Alfred has never seen Selena, so if it was his imagination, how could he have seen Bruce with her?
EDIT: Thank to the commentators - Alfred does see her at the beginning of the movie and again when Bruce shows him her profile.
And I feel it's good they didn't kill him. The minute the bomb exploded, I thought that (the) Batman was dead as the first thing that came to my mind wasn't "oh no!" but "Just like Apocalypse!" If they'd stopped there, it would be too similar to it.
Also, if we assume that he didn't use autopilot (which he most certainly did), we can do some math...
He needs to go 12 miles from Gotham City. Let's say he was a further 6 miles inside Gotham, meaning he flied 18 miles in around 2 minutes (I think the timer showed 1:54 just before he flew away). He may not even need to go an extra 6 miles, probably 4 would be enough, considering the Bat is extremely strong and sturdy. Also, after dropping the bomb, it would enter the sea, and that would dampen the effect further.
That comes to 540 mi/hr. A Bowing 777 flies as 560, so I think we can safely assume that the Bat travels much faster. The mushroom cloud could've blocked the view of the Bat, especially if he flew close to (or maybe inside?) the water.