Dressing for a public apology is different from dressing for any other public appearance because you want to portray respect, humility, and remorse rather than power and authority. But it is equally distasteful to go overboard trying to appear gentile and dapper because it is easy to cross the line to mockery.
This is particularly true if you're apologizing for the merciless beating a petite, defenseless woman who is a passenger in your rented Lamborghini.
Let's hope you never find yourself having to make a public show of remorse, especially for such a heinous and distasteful act, but just in case the media does catch on to your Brazilian mistress, performance enhancing drug usage, or acceptance of bribes, here's what to wear.
Unlike your actions your attire should be straightforward and understated. It should not scream any message to your viewing public. Your best choice is a dark grey wool suit; not black - you don't want to appear to be dressing for your own funeral. Pair it with a white shirt and a grey silk tie with a simple, subdued pattern.
Avoid bright colors. A tone on tone color scheme is unobtrusive and dignified, and provides just the backdrop you want while ingratiating yourself to the public again. Lastly, wearing anything with even a hint of flashiness will not help your case, like too much bling or say, a big Robbin's egg blue bow-tie.