Bruce quickly sneaks away to put on a hat and some glasses.
That hat and those glasses have kind of a history. In the DCAU, that outfit belonged to the Gray Ghost, a superhero-esque TV show that Bruce loved as a kid. He and the actor who played the Ghost team up to stop a bomber who's mimicking the plot of one of the episodes. The actor is shocked to find that the Batcave is extremely similar to the Gray Ghost Lair and Batman reveals that there's a corner of the cave which is just a shrine to the show. After the bombings revitalize interest in the show and rescue the actor's dying career, Bruce Wayne shows up to a signing and subtly reveals his identity to the actor.
That actor was played by Adam West.
Also the bomber was modeled after and voiced by Bruce Timm ---