Although even with a lead of 20 or 30 seconds, that still wouldn't be enough to survive a blast like that.
I'm willing to suspend my disbelief that Bruce Wayne is not in the Bat as it flies out to the bay. This would mean that when it detonates, he's probably safe on land. Since we don't see this, it's only speculation.
However, what I'm not willing to suspend is that the Bat is capable of reaching the minimum safe distance of six miles off the coast of Gotham (the bomb was previously referred to as having a six mile blast radius) when they are still on the ground with less than 2 minutes left to go, discussing what to do. The Bat would not only need to be capable of speeds well over 150mph (plausible) but they would have needed to be hauling ass and not waiting around.