There was never a single bat. The armory had more than one and we can see that Bane uses them for city patrol. When the techs check the other bat, we see that it has been patched in the auto-pilot issue. But the thing is, Bruce Wayne wouldn't have a favorite Bat and use it every night. Being realistic, it's quite possible, damages occur and that he keeps switching between them, Hence he needs the auto-pilot fixed on all of them. And I don't think he was planning on using it to destroy the bomb. It was fixed six months ago, like the tech says. It was a spur-of-the-moment thing when Bruce saw his out and decided to take it. He saw Blake stand up to the bad guys and that's when he gave the co-ordinates of the cave to him. Then he just lies to Gordon ( or Catwoman ) about the auto-pilot and takes his way out of the crime-fighting business.
As for the bomb explosion being huge, so what? He just got off way ahead near the bay. They never did show the last few seconds ticking and Batman's face together. He had enough time (close to 40 seconds). And the speed with which Bat travels, say 250 m/s ( it's a futuristic plane, it could even be supersonic but we never saw the sonic-boom ), so 40 seconds counts for 10 km. Now that's pretty safe and far off.