For the most part superheroes try to hide their true identities from the general public. Doing so allows them to lead fairly normal lives when not in costume to protect the innocent.
Contrary to many other superheroes, Superman is one of the only characters who does not use a mask to obscure his identity. Instead, he simply takes the gel and trademark curl out of his hair, puts on a pair of spectacles and assumes a ‘mild-mannered’ demeanour.
Taking the above into account, it is no surprise that Batman would begin to suspect something.