Bruce Wayne knows far too well what it is to be orphaned. It is in no small part why he's become somewhat known in Gotham for taking in orphans as his wards. And, sure, there's... ulterior motives. There's no denying many of his kids are also the Bat's sidekicks; which comes first - the 'vigilante' or the 'adopting' - varies. But when it really comes down to it, it doesn't matter whether or not the kid's prime sidekick material. He can train anyone with the spirit to learn. No, what matters is an orphan in need.
It's how it was with Dick. With Jason. With Tim. Cass. Steph, Duke... and now, with you. He sees a child who needs someone. He sees his 8-year-old self reflected; alone, scared, hurt, lost. He sees that, and he can't turn away. So he opens his home and his life and even his crusade, and takes in another orphan.
People may think he's saving them, but in truth? His family saves him, every day.
"Well, that's the grand tour." He's got a hand on your shoulder, a light touch, nothing too firm - supportive. "Alfred and Dick will have all of your things moved in soon. Hope the room's to your liking."
He's keeping his voice light, but he's watching you. Move-in day can be... overwhelming. He understands. Bruce imagines it must be a terribly complex mix of emotions. Moving into Wayne Manor. Being taken in to train under the Dark Knight. He likes to think that those would both be considered good things to you - he hopes you're glad to be here.
But he's also very aware that a part of what got you here is that you've been orphaned. And he is well aware of all that that implies. So it's... it's not all good, is it?
It's not like he can fix it. Nobody can. ...Even Alfred couldn't fix it, could he? But he can be here, and he can understand. Heh, it's worked pretty well for his kids so far, he likes to think.
"If there's anything I can do to help you settle in, you let me know, okay? This is your home now. And we're all very happy to have you."