Well, it could start off really rocky. Bellatrix is a Death Eater and Harry is the Boy Who Lived. But during the training, they might find common ground. Bellatrix could be using the training as a way to atone for some of her past sins, and Harry might start to understand that she is more than just a villain. Their relationship could evolve into a strange friendship where they both learn from each other, with Bellatrix teaching Harry about the darker aspects of magic and Harry teaching Bellatrix about loyalty and the power of love.
At first, their relationship would be full of distrust. Harry would be wary of Bellatrix as she has been an enemy for so long. But as the training progresses, he might start to see a different side of her. Bellatrix, on the other hand, might develop a strange sense of pride in Harry's progress.
At first, it would likely be extremely hostile. Bellatrix would view Harry as an enemy to be destroyed, and Harry would see her as a symbol of the evil he has been fighting against. But as time goes on, if they are forced to interact, there could be a begrudging respect that develops. For example, Bellatrix might respect Harry's magical abilities that have allowed him to survive against Voldemort so many times.
Their relationship would likely start off a bit rocky. Kakashi is a proud and skilled ninja even as a young boy, and Naruto coming in to train him might be seen as an intrusion at first. But as Naruto shows his genuine care and his own amazing skills, Kakashi would start to respect him. Eventually, they'd become like brothers, with Kakashi looking up to Naruto in some ways.
At first, their relationship would likely be formal, with Genma as the strict trainer and Sakura as the eager student. But as time goes on, Sakura's determination and progress might earn Genma's respect, and he could become more of a mentor to her. For example, he might start sharing his own experiences with her to help her understand the importance of the training.
He could develop a more cunning side. Bellatrix is a sly character, and Harry would need to learn to be crafty to survive in her world. This would be a big change from his usually straightforward and brave self. For example, he might learn how to deceive Death Eaters or other threats.
Some fanfics develop their relationship through magic. There could be a spell or a magical bond that links them. This forces them to interact and understand each other on a deeper level. As they struggle with this new connection, they start to learn about each other's motives, fears, and desires. For instance, a magical bond might make Bellatrix feel the pain Harry has endured, which makes her re - evaluate her view of him, and vice versa.
One possible plot could be that Bellatrix, in a strange turn of events, decides to train Harry in the Dark Arts not to turn him evil but to make him a more formidable opponent against Voldemort. She might see his potential and think that by teaching him some of the Dark Arts, he can better understand Voldemort's tactics.
His character would be under great pressure. He might become more secretive and cunning as he tries to hide his true feelings. Since Bellatrix is so unpredictable, Harry would need to be on guard all the time, which could make him more paranoid than the normal Harry we know.
It could start with hostility. Since Bellatrix was a Death Eater and Hermione was on the side of good, the daughter might inherit some of her mother's prejudices. But as the story progresses, they could find common ground, like a shared interest in magic theory or a mutual friend. This could gradually lead to a more amicable relationship.
Harry would likely be more conflicted. With Bellatrix's influence, he might have a darker edge to his personality. He could be more aggressive in his approach to problems. Sirius, on the other hand, would try to keep him on the right path, so there would be an internal struggle. He might not be as quick to trust as the original Harry, but more cautious and calculating.
In a time travel scenario, their relationship could become a complex love - hate relationship. Bellatrix may find herself attracted to Harry's courage and determination in a different way than she's used to. Harry, while disgusted by Bellatrix's actions in the original timeline, may start to see a different side of her when they are in a different time period. This would be a very strange and morally ambiguous relationship, full of internal and external conflicts.