Bruce knows that John Grayson is Dick's father, not him. He knows that, Dick knows that. He's okay with it. He doesn't want to replace Dick's father; he could never do that.
But sometimes, he truly wishes he were. Who wouldn't want to be the father of such a wonderful child?
In any case, in his mind, Dick is his son; even if he isn't his father.
That's why he never asks to be called anything other than "B" or "Bruce," because he's not Dick's father, even if Dick is his son.
That's why, when Dick woke up from horrible nightmares screaming "Dad!", Bruce would run to his room, hug him, and comfort him.
Dick might sob, repeatedly telling his dad not to leave him alone.
Bruce wouldn't correct him, he wouldn't push him away... And selfishly, he would always reply, "Here I am, I'm not going to leave you".
Because he wouldn't do it, even if Bruce is not really his father... He's still Bruce's son.
When Dick was hurt and scared from a fight gone wrong, and half-sedated he would call for his dad, Bruce would take his little hand and whisper to calm him down.
Dick could offer apologies to his dad, but Bruce would never accept any.
Bruce doesn't tell him he doesn't accept his apology because he's not really his father. But Dick is his son.
Every time Dick says "dad" absentmindedly, Bruce swallows and answers, without correcting him. He understands that Dick is probably unaware of what his mind is doing to him, that he keeps calling for someone who is no longer there.
And Bruce, being the selfish man that he is, convinces himself that this is why he doesn't correct him, and not because he fervently wishes to be his dad.
It is not until Dick becomes an adult that Bruce is proud of, such a wonderful person, a man worthy of admiration... that he realizes it.
It is when Dick is telling someone a story about his parents that Bruce notices the pattern.
Dick never, ever calls John Grayson "dad".
He uses variations of the word, mostly in what he knows is Romani, sometimes in French... But never English.
John Grayson is never called "dad", not even once.
Only then does Bruce Wayne realize.
Bruce may not be Dick's father...
And he knows for sure, that Dick is definitely his son.