The first time he realizes it, Bruce feels sick. This is a child. An orphaned child he brought into his home for a number of reasons, but not to start feeling things that are reserved for adults.
He tries to ignore it at first, and when that proves impossible he tries to cut himself off from the boy, be distant - but it's just so impossible, just because it's Dick. He brings light to the manor after years of darkness and fills the quiet halls with laughter and joy. He brings life and love and everything that just makes him him. So Bruce buries the feelings deep.
He realizes it's love when he never feels the same thing for Jason or Tim. They feel more like sons, not the other half to a missing part. Dick and him barely speak by that point though, their relationship so damaged it might be beyond repair. He's a afraid too, even though Batman should never be afraid.
It's not just what people will say in their lives as Bruce Wayne and Dick Grayson, it's what people will say in their lives as Batman and Nightwing. They'll probably question if it started when Dick was a Robin, if the rumors are true about the relationship between Batman and all of his Robins. There will be scandal all around. Headlines about "Bruce Wayne and His Ward" and whispers about "Batman and Robin's activities in back alleys."
He feels he isn't good enough for Dick anyway. He's broken beyond repair, he's fucked up. He'll just drag Dick down with him, and gone will be the sunny, positive boy he fell in love with.
So Bruce keeps burying those feelings deep, even when sometimes it's hard not to reach out and touch, even when he knows that having Dick in his life will make it exponentially better.
Because sometimes it's easier to hide, than it is to love.