In the final fight between Batman and Superman in Batman V Superman: Dawn of Justice, Superman addressed Batman as Bruce which is his true identity. How did he know Batman was Bruce Wayne?
It's strongly implied when Clark/Superman can hear Alfred talking to Bruce during Lex Luthor's party (when Bruce starts snooping around so he can hack into LexCorp's mainframe) that he is realizing that Bruce Wayne is Batman.
Also I would venture to say their conversation at the same party suggests that both are on to each other about the other's identity (as evidenced by the direct question from Clark to Bruce about Batman, and Bruce mocking the Daily Planet's love for Superman).
I don't believe there's any explicit evidence in the film, just suggestions. That said, if everything in a movie is explicitly stated, that kind of takes some of the fun of interpretation out, right?
It's not explicitly stated in the film but it can be speculated that he got it in the party.
He heard him talking to Alfred and maybe by the conversation he made his speculation about his secret identity. He even stopped him from stealing Kryptonite, so he might have done all his research from the time of party to this point of time. And it was no tough for him with his super-hearing.
I think it is a bit like the video game Batman: Arkham Knight. After you rescue Jim Gordon, he somehow knows Batman's true identity, You never figure out how he knew but, there was evidence of Batman talking to Alfred, and just like the party scene in BVS Clark knows about Batman's identity by just doing the simple and putting two and two together.