He had, of course, been in the middle of something important (a particularly grueling chase down Gotham's side streets) when Passages decided to expel him out into the lobby, which meant that a militarized version of the Batmobile plowed through the hallway and nearly took out an entire flight of stairs before grinding to a halt. The interior of a building obviously looked nothing like his familiar streets at night, and after nearly fifty pounds of armor and black emerged from the vehicle to assess the situation, it quickly became evident what had occurred. His door was no longer accessible--breaking it down accomplished nothing--and this was not Gotham. He recognized where he was, because Luke did, and he was not pleased about it in the slightest.
Then came the discovery of the ice-coated streets, which the Tumbler could fortunately manage quite well, and the beast that appeared out of nowhere; neither of which served to improve his mood. Luke's voice was much fainter than it should have been, but he was worried about his son, and while the Bat had no particular fondness for children he could understand the boy's concern. Had it not been for the disaster in the streets, his arrival would have been much faster. To ignore those in need was simply not in his nature, however, and by the time he was speeding towards Luke's apartment building there was already a cluster of people babbling excitedly about having been 'saved' by Batman and he had, unfortunately, learned the hard way that his suit did not hold up very well against dragon venom.
Never one to utilize front doors unless absolutely necessary, the Bat came in through the window, arriving just in time to see Gus free Finch from his closet prison and advance upon the two women. His gaze was quick and sharp as it darted about, absorbing all the details; Iris, whom he recognized thanks to Luke's memories, Selina and her straight jacket, the snarling dog, and the little boy, who lit up and began babbling excitedly at the sight of Batman himself standing in his room.
The Bat was not exactly a fan of dogs, but he had no intentions of hurting this one unless it became necessary. "Finch." He may not have had Luke's voice, but his was all thunderous command, enough to strike even Gus silent, and the dog turned with a growl at the sound of his name. "Down," he demanded, and while the dog recognized an alpha when he saw one, he bared his teeth in defiance regardless. On top of everything else, it seemed, he was now engaged in a standoff with an animal, but at least his attention was diverted for the time being.
"Stay still, both of you. Especially you, Selina." While the Bat hadn't been around to witness the entire show, he wasn't called the world's greatest detective for nothing.