No, there has to be two. The one that Batman uses throughout the movie blew up with the bomb. Afterward we see Lucius talking with the two techs that are looking at the Bat prototype when they tell him the autopilot was already fixed. The one in that scene is the prototype that Lucius showed Bruce early in the film. It has a grey paint job instead of the black that Batman's does.
One highly plausible answer to this is that after the city is restored, the Applied Sciences division builds a new prototype to replace the one that was obviously missing. The software package they upload to it would come from a server. So Bruce patched the autopilot on the server, and then downloaded that to his Bat, which at the time was the only one in existence.
As far as the paint color, it could be that they painted Batman's black, but the new one is the same gray color that came off the assembly line.