Originally Posted by Antithesis_SD
One idea I had is that they first encounter one another when Batman sneaks into a LexCorp or STAR lab to investigate... something... and Superman ends up there trying to stop someone (I clearly haven't thought it though yet), and there is a bunch of Kryptonite in the lab. It's the first time Superman has encountered Kryptonite, and so not only is he surprised to see the fabled "Bat-Man of Gotham," but also that his powers aren't working and he can't see through the cowl due to the radiation sickness. Batman, noticing the apparent fatigue, slips a piece of the rock into his belt for a later time and sneaks out while Superman deals with the lab' advanced automated security. As for finding out each others' identities, I haven't really mapped anything out, but I can't see how they wouldn't in the movie.
Its an interesting idea to have them both discover kryptonite at the same time.