It was subtle and probably understated, I think Nolan wanted the audience to piece it together from little things & then have a big "Oh, NOW I get it! Very clever!" moment, but most people didn't. I had to re-watch it twice to get it all, trying to make sense of it, b/c I had the exact same reaction the first time.
Bruce isn't in that Bat when the bomb detonates. Lucius tells him earlier in the movie that "a better mind" (like Bruce's) would be needed to get the remote-control function for The Bat operational. It isn't shown explicitly, but clearly Bruce does this, there's a scene where a puzzled Lucius mentions Bat prototypes (proving there are other Bats, even if some are more advanced than others) being programmed with auto-pilot tech, by Bruce. In the final scene, he is remote-controlling the nuke-carrying Bat, while he's in a second Bat.
He is shown entering the Bat that carries the nuke, yes. I don't see nearly enough people noticing/mentioning this next part, though: A short while into his flight (long enough to get out of visual range of any witnesses), he pushes a button on his flight controller, and that launches a missile at a building. That isn't so that he can clear the building: That is his smokescreen, that is when he exits the Bat, and begins operating it remotely. "Theatricality and deception," & all that. You then see him in the cockpit of a Bat that is flying, and the editing cuts lead you to assume it's the same Bat that's carrying the nuke. But it isn't. The proof is flimsy, and I'm not arguing that it's well done, but it is what Nolan wanted us to piece together:
If you watch his face when he's in the cockpit after that explosion, look at the light & shadow playing across his face. The Bat carrying the nuke emerges from the smoke of the expIosion, passes over Blake & the schoolbus on the bridge, and then goes out to sea. If Batman were in that Bat, his face should be evenly lit from that point on - the only light source is the sun, no buildings on either side of him, no explosions, no lightning. But then the camera cuts from the Bat & nuke, to him in a moving cockpit, and instead of even lighting, you see surges and flickers of light on his face... Because the Bat that he's actually in, is flying back through the city, between buildings (some of which are on fire).
I didn't get it the first time, either. Nobody in the group I saw it with could figure it out. And if I weren't OCD about trying to piece it together, I sure wouldn't have. I thought Nolan was a better filmmaker than that, and it turns out he is... he's just too subtle for his own good sometimes. I actually think the whole reason Batman does the silly smoke-bomb trick in his first fight with Bane (I get it - he was desperate & losing, but those were some lame smoke-bombs!), is so that the concept of smokescreens & misdirection is put into our head. It also obviously gives Bane an excuse to reiterate "theatricality and deception," so that it's in the back of our minds for the Bat finale.
My 2 cents, anyway