I know that Bruce having the Brucie persona is like a whole thing, but I kinda wanna see... A Bruce that comes back from his training, spends a year or two building the promiscuous playboy routine, only for Dick to show up and Brice gives it all up to basically become a soccer mom. Like, one day, Bruce is playboying it up, taking a date to the circus, only for tragedy to strike, and Bruce abandons his date to shield the little boys eyes. Then Bruce is gone for a week, no sightings at all, as rumor spreads he's adopted that boy. And when he finally shows up at a fundraiser gala, he's twitchy and nervous. And someone asks, and even if he's Batman, Bruce can't help but let it spill that, "oh, Dickie didn't want to come, but I've never left him for this long before, and Alfred said he'd call if Dickie asked for me, but it's been an hour since I left, and I haven't heard anything, and what if something's wrong?!"
And people are blinking, confused. They've never seen smooth talking playboy Brucie Wayne like this before. Someone offers him a drink, and he turns it down, because what if he has to drive home quickly?! What if little Dick Grayson gets scared in that big house, and he wants Bruce to come home?! He can't drink, are you crazy?! So someone tries seduction, asks if they can "give Bruce a distraction", only for Bruce to zero in on that person, and whip out a plethora of pictures, all of Dick, and start talking nonstop about how amazing his boy is, and how cute he is, he's 9 and an acrobat, and he's just so talented!
And then, for the rest of the time Bruce is there, he's bouncing between guests, and from a distance it seems normal. He's in peoples bubbles, he's smiling, and looks like he's flirting. But get a little closer and you hear him just cooing about his new sweet baby boy. And it doesn't matter that Dick is already 9 or that Bruce has only had him for a week, if anything happened to his baby, he would just die!
And eventually, Bruce leaves, and people expect that, when the 'new mom' energy leaves him, Bruce will go back to his promiscuous ways. But it never happens. Bruce still acts like an idiot most of the time, but now instead of "idiot with only sex on his mind" he's an "idiot that can't stop talking about his kid". And it's only kind of an act now. Bruce enjoys talking about Dick, and he loves spoiling his son. But sometimes he's just at a regular gala, and an old flame tries to flirt, and it goes right over Bruce's head and he ends up showing off pictures of Dick instead. In the following years, only one person (Talia) manages to get in Bruce's pants in the years that follow Dick's adoption, and she only manages because she pretends to be a maternal figure just as proud of Dick as Bruce is, and Bruce gets distracted enough by someone else acknowledging Dick that he falls for it. After that, Dick becomes kind of protective, and keeps butting in when people are flirting with Bruce in public, and Bruce never dates anyone Dick doesn't approve of.
But their relationship isn't perfect. Dick is still Robin, and Bruce is still Batman. They have a good relationship, but as Dick gets older, Bruce continues to be protective. Maybe even too protective. Batman takes hits for Robin that he doesn't need to. He makes plans that put Robin in the least amount of danger, even if it makes the plan actually bad. He's more anxious when Robin gets hurt, and tries to bench Robin for the smallest of injuries. Bruce and Dick have a falling out still, because Dick is 18, and he can handle these things on his own, and he needs space to grow on his own now. But Bruce just can't help but be a helicopter parent, especially when in costume. So Dick leaves, tells Bruce not to follow, and he disappears for a few months. And Bruce, who's so used to having a kid to love and coddle, is lost for a while.
Until he finds Jason Todd stealing the tires off the Batmobile.