In all honestly, Bruce hadn't had any reason to investigate Daggett Labs. Not until a run-in with Selina Kyle had given him reason to be suspicious. Selina might be the sort to act in her own interests above much else, but the Dark Knight knows enough to recognize it would be foolish not to put at least some stock in her intel. If this place had drawn Catwoman's attention, something was going on, and for as much as Selina was a thief and a criminal... well, he'd seen enough to know that she wasn't a bad person. Misguided, maybe. But what would she have to gain from lying to him about an animal-napping scheme?
It had been enough to get him to have Lucius look into it, at least, and find rumors that the laboratory was developing some unknown drug. The lack of information beyond that was suspicious in and of itself, and in a way Bruce found... concerning. And that had been enough to have him using tonight's patrol to come investigate things in-person, driving the Batmobile along the snow-covered roads out to the lab on the distant outskirts of Gotham.
Well, that had been the plan, anyway. That plan had been interrupted when he spotted the figure stumbling through the snow - he hardly had a chance to get a look before they'd all but collapsed in the road. Well of course he was stopping to investigate. He's quick to climb out of the car and hurry over.
Bruce could claim he was surprised to recognize Catwoman's distinctive costume - on some level he was, but only because of present specific circumstances. Was he surprised she'd gone against his advice and come out here herself to nose around? Not at all. Was he surprised to find her half-passed out in the snow? Yes. Surprised and concerned, even if he wasn't likely to be immediately forthcoming with the second one.
"Catwoman? What's happened? Are you alright?"