The Clown Prince of Crime
Super Freak
The US government should probably know after the events of MOS anyway. Doesn't he tell them his age and where he grew up?
If that didn't do it, Superman hugging his mom in her home while Lois calls him Clark right in front of the military guys should be enough I guess Batman can get access to all the military records, but assuming no one except Lois knows his identity, it's going to be pretty ridiculous if Batman, the world's greatest detective meets Clark and doesn't recognize him as Superman.
I just don't see why a brooding, loner character that these movies tend to depict would team up with super-beings.
Maybe to learn their weaknesses and to keep an eye on them. Batman always has ulterior motives, so I could see him "playing along" and being a team player, but really, he's just gathering information and working on a contingency plan. Remember, he sees them all as a potential threat...and he probably doesn't trust them yet. So for now, he
Keeps his friends close and his "enemies" closer.