Oh, no. It's even better. Read all of this for maximum effect, but if you just want to see why he wears the suit, skip down to the bold.
Synopsis: Dick Grayson is casually walking down a sidewalk when he hears someone yell that a group of thieves are getting away. Dick contemplates changing into Robin, but has no time to when the thieves' getaway car speeds towards a young girl crossing the street. Dick rushes to the young girl and gets the both of them out of the way, but bangs his left elbow on a lamp post in the process. A doctor arrives on the scene and informs Dick that his arm isn't broken, but he will have to lay off it for a week. Later at Wayne Manor, Bruce and Dick watch a news report about the robbery that includes a piece about Dick's heroic act. Dick tells Bruce that he saw the thieves' faces and would be able to identify them, however a search of their crime files turns up nothing. As the stolen item was a camera, Bruce deduces that the thieves must be planning a larger crime at an event that will attract media attention. He and Dick plan to attend such events with Dick keeping a watchful eye out for the thieves.
In carrying out their search, the public is puzzled as each event sees Batman wear a differently colored Batman costume. During a parade, Batman wears a red costume. While saving a block from the threat of an explosives truck aflame, he wears a light blue costume. Batman steals the thunder of a movie star and a set of valuable jems when he appears at those events wearing gold and orange costumes respectively, causing the public to think that is Batman's reason for his colorful costumes. It appears the thieves have caught on to Batman's plan when Batman has to save a launched ship and when Batman is shot while attending a sharpshooting contest. That last one was really Batman's fault as he was wearing a costume with a bullseye on it (don't worry, he was wearing a steel vest underneath).
After the last event, the story cuts to the thieves being pursued by the Dynamic Duo where we find out that they will really be striking at a money show to snatch up $1,000,000. The next day at the money show, Batman arrives wearing a costume that is truly a rainbow costume. As soon as one of the thieves walks in, Robin identifies him and Batman gives him a red left hook. Batman finds a gas mask on his person and realizes that the stolen camera is booby trapped with gas. Sure enough, the stolen camera is found with tear gas inside it and Batman and Robin take down the other two thieves. Back at the Batcave, the reason for Batman's colorful costumes is revealed: to prevent the connection between Dick unable to use his left arm and Robin unable to use his left arm, Batman wore brilliantly colored costumes to focus all attention on himself and allow Robin to freely search the crowd for the gang of thieves.