One reason could be that Bruce Wayne never had the traumatic event that led him to become Batman in the original story. Maybe his parents' death was prevented somehow, so he never felt the need for vengeance and justice in that extreme way.
Well, in such a fanfic, it might show Bruce Wayne as a completely different entity from Batman. Maybe Bruce is just a normal rich guy who has no idea about the vigilante activities of Batman. He could be living his own life, focused on business and social events, while Batman is someone else entirely, perhaps an unknown figure with no connection to the Wayne family.
Bruce Wayne in Batman Begins fanfiction is often a complex character. He is a man on a journey of self - discovery and vengeance. In fanfiction, we might see different aspects of his training that were not fully explored in the movie. For example, his time with Ra's al Ghul could be delved into more deeply, showing his internal struggle between the teachings of the League of Shadows and his own moral code.
The dynamic could be complex. Thomas might be both proud and worried seeing Bruce as Batman. Proud that his son is carrying on the legacy, but worried about the dangers. He could be overprotective at first.
One possibility is that Thomas Wayne Batman comes from an alternate timeline. He meets Bruce Wayne in the current timeline and shows him a different way of approaching crime - fighting. Maybe he has more brutal methods, which causes Bruce to question his own more restrained approach. They could then learn from each other and create a new, more effective Batman strategy for Bruce's Gotham.
The author might introduce a new character to take on the role. Maybe a completely unknown vigilante steps up. This new character could have different motives and methods compared to Batman. For example, they could be more focused on preventing crime through community outreach rather than the intimidation tactics Batman uses.
In this fanfiction scenario, Poison Ivy may initially be angry. She might feel betrayed if she had some sort of relationship with either Bruce Wayne or Batman before. She could also be a bit jealous, thinking that Batman has been hiding this huge part of himself from her. However, on the other hand, she could also be impressed by the lengths Bruce goes to protect the city. This new knowledge could lead to a whole new dynamic between her and Batman, with her either becoming an ally or an even more dangerous foe, depending on her motives and the events that unfold in the fanfiction.
One of the most intriguing Bruce Wayne fanfiction stories in the Batman Begins universe is those that focus on his pre - Batman days. Stories that show his travels around the world, learning different fighting styles and philosophies. For instance, a story might detail his time in the Far East, training with martial arts masters and how that influenced his later combat techniques as Batman.