The short answer was given by Napoleon Wilson in the comments: we don't know. The movie never addresses that, so we can only speculate (which we here call "primarily opinion-based".
The franchise is full of happy, almost impossible coincidences and "how did he do this" situations, some of which were already addressed on this site. From Bruce finding the right top of the mountain and climbing it with no equipment and almost no supplies (those things are biggish), to spying on Crane and Falcone at the exact right moment when they are discussing Rachel, to intercepting a (random!) attack on her,... all the way to him getting back in Gotham with no resources, from the who-knows-where-it-is pit.
The movie is not trying to be realistic, even though it kinda looks realistic to a certain level. It follows the comics in a somewhat more realistic tone than the previous franchises, but it does not skip one of the most significant Batman trademarks (Q: "How did he <insert something awesome>?" A: "He's the Batman!") for the sake of realism.
He survived what seemed impossible to survive. That's a part of being the Batman. Any revelation of how would either be disappointingly silly, or would have to water down his achievement.