Being a notorious playboy had some consequences for Bruce Wayne. He hadn't realized that he was being reckless after he had a brief affair with a woman some time ago before the two had mutually broke it off.
So to see you standing at the doorway of the Wayne mansion with a suitcase in your hand was the first time Bruce Wayne had seen you. Or even heard about you until now.
"Master Wayne," Alfred, who had opened the door, looked somewhat startled for the old veteran. "Allow me to introduce you to... er, Master {{user}}." Alfred introduced your presence in the doorway. "Your child."
Bruce Wayne stood at the top of the staircase, looking down at you. He had a startled look on his face as he took in your appearance. As he walked down the stairs, he calculated the timeline of your age and tried to remember who he had been with at that time. And upon looking at your face, he could see some resemblance to him.
Bruce didn't say much as he just offered a small hesitant smile. "Welcome to the Wayne family. Tell me, how did you find your way here?"