Often, she is depicted as being just as intelligent as the male Bruce Wayne. For example, she has a sharp mind for detective work and strategy. She might be able to quickly analyze crime scenes and figure out the motives of the villains.
He might develop a greater sense of humility. Without the Batman persona to fall back on, he has to face his own limitations as a person. For example, he may struggle to get people to listen to his ideas for change when he doesn't have the intimidation factor of Batman.
One great fanfic is 'The Father - Son Bond'. It beautifully explores the complex relationship between Bruce and Damian. It shows how Bruce tries to be a good father while also dealing with his role as Batman, and Damian's struggle to fit into this new world with his own strong - willed nature.
Patrick Bateman is not a real individual. The character was created for the satirical and disturbing narrative of 'American Psycho'. The story uses Bateman to critique consumerism, shallowness, and male violence in 1980s yuppie culture. It's a work of fiction that plays on the excesses and dehumanization of that era.
The plot is also important. It could involve them facing a new villain or a threat to Gotham that tests their relationship. Maybe a situation where Damian's actions put him at odds with Bruce's code of ethics, and they have to work through it. This kind of plot tension can make the fanfic really engaging.
The key elements of the Patrick Bateman story start with his status - seeking nature. He's desperate to be seen as the best among his peers in the cut - throat world of 1980s investment banking. His narcissism is off the charts, constantly preening and comparing himself to others. The violence in the story is not just for shock value but also to show how the pursuit of wealth and status can lead to a dehumanized state. His relationships are all superficial, like his interactions with his fiancée and colleagues, which is a mirror to the soulless nature of the yuppie culture at that time.
At first, it could be a bit rocky. Bruce is used to his own way of doing things and Buffy has her own independent streak. But they would gradually learn to respect each other. Bruce might be impressed by Buffy's combat skills and her ability to handle the supernatural. Buffy, on the other hand, could learn a lot from Bruce's strategic thinking.
Believable young Bruce Wayne is about showing his evolution. Start with his basic characteristics. He's smart, already showing signs of being a prodigy. But then add in the emotional aspects. He's angry about what happened to his parents but channels that anger into something positive. He might start small, like helping a neighbor who has been robbed. His relationships with other kids his age are also important. He might not fit in completely because of his different mindset. And his growing obsession with bats could be a unique quirk that you play up, as it ties into his future identity as Batman.