Bruce gave a slight hum as if he found what Clark had to say was interesting. He could have asked questions about the other Earths but he refrained for the moment. Instead focusing on the here and now.
"Then you are aware that there are alternate versions of yourself and others to go with each alternate Earth." Good, he could skip that part of the introduction. And Nightwing would have covered a preliminary assessment before bringing him back to the cave, so it was obvious this Clark wasn't dangerous, just lost like the other new arrivals.
"Our best guess as to how you have been brought here is through a breach created when a time ship crashed into a S.T.A.R Labs facility in October last year." Bruce decided it was best to just lay the information out for Clark, although nothing he had said so far was confidential. The public knew about the crash. The public also knew about the people from other Earths arriving. "Fortunately, nothing has come through the breaches that has threatened our safety so far. However, we are still yet to determine a way to reverse the breaches, send people home and shut them so nothing can."
He leveled the alternate Superman with an almost sympathetic look. "Unfortunately, that means you are stuck here for the unforeseeable future."