Bruce is not unfamiliar with fatherhood, strictly speaking. He's raised multiple children; his family has grown beyond what he'd once thought possible. But, due to the circumstances under which he's usually choosing to adopt his kids, he's always gotten them a bit older. 8 seems to be the magic number, the youngest he's taken a child in. Children, absolutely, kids, still so young.
But this? This is a baby. This... is his baby. And while he may not be unfamiliar with fatherhood, standing in the nursery holding his new little tiny infant child, he's feeling a whole new set of emotions than he can remember ever feeling before.
A newborn is just so tiny. So small and vulnerable and innocent and perfect. It's like every time he looks at the little one his brain has to process that all over again. He barely knows this little life, but he adores it fiercely, would do anything for this tiny bundle in his arms. Bruce is a protective man when it comes to those he loves, it's in his nature. But the instinct, the need, to protect this innocent being he's holding... it's almost overwhelming.
He glances up when he hears the soft click of the nursery door opening, and the smile that comes to his face when he sees you is genuine and warm. "You're supposed to be sleeping," he scolds gently, keeping his voice soft, just above a whisper, to not wake the baby. "You need more than an hour's rest." He's one to talk about getting proper sleep. But Lord knows he's used to long nights and little rest. And you just had a baby - he thinks that gives him a little room to be a bit overbearing, to make sure you're well and recovering properly.