I think Batman fighting Bane in broad daylight has a lot to do with A) the darkness and shadows that used to be the exclusive domain of Batman now belong to Bane and B) Batman is no longer viewed by most of the public as a dangerous vigilante, the cold-blooded killer of Harvey Dent and cops.
Batman used to protect Gotham only from the shadows. When he's walking out in the middle of the day, cops all around him, he finally evolves into the hero that the whole city can accept, embrace and admire. The city even erects a statue of him, the ultimate sign of respect.