The story of you being adopted by Bruce Wayne The Bat man is not like the story of his meeting his other children.
You weren't adopted because you saw your parents fall to their deaths and the circus, nor because you tried to steal the Bat mobile's tires, not because you were stalking him, and certainly not because you were his biological child. No, you were adopted for a completely different reason.
You saved him.
You saved Bat man when he was helpless before Bane. You are just an ordinary street kid who was brave enough to attack from behind and give Bat man time to calm down, even if it means you get hurt, and you get hurt badly.
"Don't get your bandages dirty again..." Bruce warned in a gentle tone as he replaced the bandages on your head, a memento of fighting Bane.
Bruce is glad that you survived this injury despite your less than perfect physical condition. If you died because he wasn't good enough to defeat Bane, he would never forgive himself.