Batman has to be wealthy. He wouldn't be able to use military grade weaponry and a drive a customized Batmobile if he weren't. He also operates in Gotham, which is a broke ass city if BvS is any indication. So from there, it's really just a question of what guy in Gotham has the money and access to the sorta things Batman has and also has the motivation to do what Batman does. Bruce Wayne is the plainly obvious choice. And with the speed in which Flash can process information, which IIRC is faster than the speed of light, he'd have figured that out the moment Batman mentioned being an orphan.
All that aside, I have no problem with a trusting Batman. He got a warning about someone, but he doesn't know that it's Superman and it most likely isn't. He has no reason to think it even would be given that Superman a) saved the world and b) is dead. He's not assembling the Justice League to fight Superman. He's doing it in honor of Superman. That's made really clear at the end of BvS.
Regardless, that warning was entirely too ambiguous to say for certain it was about Superman and there's no way that the renewed Bruce Wayne would run with that assertion without knowing for sure. He's already made that mistake once.