As previously promised, it's time to examine, one by one, whether our heroes can dance. Let's start with Batman. Can Batman dance?
The off-the-cuff answer is obvious: "Don't be an idiot; Batman can do anything." Batman can diagnose your injuries while you're falling through space. Batman can make a telephone out of some loose change and a glass of saltwater. Batman can open a safe with his teeth, kill you with one kiss, and assemble a bat-baby-crib without any instructions. Batman can do anything.
It's probably more accurate to say, "Batman can do anything the story needs him to do." But there is a subtle "running joke" that crops up now and again over the last 60 years of Batman: Batman knows how to do everything obscure, but some times normal things escape him.
Oh, it's subtle and seldom important; little things, really. Batman can't sing (except for the one on JLU). Batman knows about movies but never watches them. Batman (or at least Bruce Wayne) doesn't understand children. Batman knows nothing about video games, baseball, or popular music. In short, the implication is that Batman has no time for anything purely fun or frivolous. Makes sense; why would he?
Dancing surely falls into the category. Why would Batman know how to dance?
Simple. While Batman has no reason to know how to dance, Bruce Wayne has every reason. Dinner and dancing with the ladies is Brucie's bag. It's all smooth and suave when you're out with BW, and when Bruce asks the band to play, he dances to the bossa nova, the music of complacence.
Besides, you just know Alfred was giving Little Brucie ballroom lessons in waltz and foxtrot from age 7 on. "Come, Master Bruce! The terpsichorean arts are a mainstay of any young gentleman's education and a key that will open many social doors. Now, on this go-round, maintain the frame of dance with a firm but not rigid steadiness of the arms ... and mind my feet, please."
Besides, the squarest version of Batman ever, Adam West, could not only dance, but spontaneously invented dances out of whole cloth, while drugged, to which entire websites are devoted.
So you better believe Batman can dance. Batman stays up late at night in the dark recesses of the cave, playing that bongo vinyl LP that Jack Knight gave him after their Solomon Grundy adventure, inventing all sorts of avant-garde dances that subtly incorporate martial arts maneuvers, just in case he needs to disarm a roomful of tuxedo-clad ninjas while in his Bruce Wayne identity on the ballroom floor.
Just in case.