This is who Batman is. Yes, he beats the crap out of criminals and deals with the Joker on a weekly basis, but that’s just his job. What makes Batman BATMAN is his incredible compassion. Bruce became Batman so that no child would ever have to go through the kind of crap he did as a kid, a silent protector of a city in hell.
Bruce takes in “strays” because he sees himself in them, sees their loss and their pain and he can’t stand it. He wants to help. Just because his persona is a fearsome, stand-offish character doesn’t mean that Bruce himself is that way, though he is definitely somewhat emotionally stunted. Bruce’s problem is not that he has no emotions; it’s that he has TOO MANY emotions too strongly and never learned how to properly deal with them. He’s an incredibly passionate person in so many ways, but he doesn’t know how to properly work through and give off the emotions he feels.
And more than anything, Batman hates to see a child in pain, regardless of who that child is. And especially with a child that has been used and abused as much as Ace had…Bruce can’t bring himself to harm that child (or any child, for that matter). And instead, he sits with her until she dies peacefully, holding onto the hand of someone who cares…because everyone deserves to leave this world with the knowledge that at least one person that cares about them.