She can play the role of a moral compass. Since Bruce is often in the gray area when it comes to his methods of fighting crime, his baby sister could be the one to remind him of the importance of staying on the right side of the law in a more emotional way. For example, she might object to some of his more extreme actions.
Often, in fanfiction about Bruce Wayne's baby sister, she is given a distinct personality. She could be the sweet and innocent type that Bruce feels the need to shield from the dark world he inhabits. Or she could be a bit of a rebel, not wanting to be coddled by her big brother. This character can add new layers to the Batman universe, creating different storylines and relationships within the family.
One possibility is that their baby grows up in a world full of duality. Since Bruce is Batman and Selina is Catwoman, the child might struggle with the two different legacies. They could inherit Bruce's sense of justice and Selina's independence and slyness. Maybe the baby has to deal with the public's expectations as the child of two such iconic figures in Gotham.
Their relationship could be shown as very protective. They are both fiercely protective of their baby and this brings them even closer together. They support each other in parenting decisions and in protecting their family from any threats.
Bruce's life as Batman would change drastically. He would now have someone depending on him not just as Bruce Wayne but also as Batman. He might have to cut down on his nightly patrols or find more secure ways to keep the baby safe while he's out fighting crime. He would also be more motivated to make Gotham a safer place for his baby to grow up in, so he could focus on taking down the major threats to the city more quickly.
The baby could be a motivation for Naruko. For instance, if the baby is in danger, it can drive Naruko to become stronger and fight harder to protect it.
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.
Bruce Wayne has been depicted as having a sister in certain comic iterations. For example, in some versions, a character named Martha Wayne Jr. is introduced as his sister. However, this isn't a consistent element throughout all Batman comics.
A possible plotline is that the baby is a key to unlocking an ancient secret in Gotham. Bruce Wayne has to protect the baby from various villains who are after this secret. Along the way, he might get help from his usual allies like Alfred. The baby also starts to bond with Alfred, creating some really cute and heartwarming moments in the story.
She could be a source of emotional support for Bruce. In the movie, Bruce is often alone in his journey, but with a sister, she could be there to comfort him during the tough times, like after his parents' death.
One interesting fanfiction could be where Bruce Wayne's little sister discovers his secret identity early on and has to keep it a secret herself while also trying to help him from the shadows. Maybe she uses her own unique skills, like being a computer genius or having a talent for martial arts.