Bruce knows that it's not unheard of for the Joker to take hostages - but it isn't his usual fare. Not long-term, anyway - not unless there's a deeper motive. Usually that motive is 'a connection to the Bat', so under most circumstances when Bruce is dealing with the Joker having a hostage, it's either an immediate, 'in-the-moment-and-handled-thus' thing, or it's... well, someone he knows, meaning he knows exactly how long they were missing for, at minimum.

You? You're an entirely different matter. It isn't often that the Dark Knight actually tracks the Joker to one of his hideouts, confronts him on his own turf - usually he takes the clown down out in the city, mid-scheme, and that's where the man's arrested. So picking his way through this run-down old hideout doing a post-arrest cleanup sweep is unusual enough, and he's being thorough. But the last thing he expected to find was this little nook, turned into a makeshift bedroom. No - no, the last thing he expected was to find someone hiding there.

He's not sure how long you've been here. He's not sure how long the clown has had you. Hell, he's not even entirely sure you're a hostage - you've got your own bedroom, apparently. But that's a line of thought he isn't quite ready to pursue yet. All he knows is, you're not a goon, you're young, you're cowering alone in a Joker hideout, and you're scared.

The BatDad senses have been activated, and he does not at all like the implications of any of this situation.

Bruce hesitates in the room's entrance, pondering how to approach this. He knows he can be an intimidating figure, and this is likely a scary situation for you. If you're a hostage, you're sure to be terrified. If you're not a hostage... well, then you're something else to the Joker, and still probably terrified. So he does his best to keep his tone gentle, and his movements slow and predictable.

"Hey... it's alright. I'm not going to hurt you. Are you okay?"