Another reaction could be that he tries to hide his pain. Jacob might put on a brave face in front of Bella and the others, but deep down he's really hurting. He could keep his feelings bottled up until it eventually explodes in a moment of weakness or when pushed too far.
Well, at first, Edward would be in shock. He wouldn't believe that Bella actually left. Then, he would likely start to search for her frantically. He might go to all the places they used to go together, hoping to find her. His reaction could also be one of self - blame. He would think that it was all his fault, that he didn't protect her well enough or love her the right way. As time passes, he could become more resigned to the situation. But he would never really forget her. He might even try to keep an eye on her from a distance, just to make sure she's okay, even though she left him.
She might be portrayed as a villain by showing her being manipulative. For example, she could use her relationship with other characters to get what she wants, like using Edward's love for her to control his actions or decisions.
Well, in some fanfictions, she might be depicted as the devil through her actions. Maybe she's shown as being manipulative, using her charm to get what she wants from others, much like how the devil is often portrayed as a tempter in traditional stories.
Edward could be one of her allies. He could use his vampire abilities such as super - speed and strength to assist Bella in dangerous situations. His centuries - old knowledge could also prove invaluable in understanding the motives and actions of the CIA's enemies. Another ally could be Jacob. His shape - shifting abilities would give the team an extra edge in combat or in covert operations. He could also use his connection to the werewolf pack to gather information from areas that the CIA might not have easy access to.
In this fanfiction, Bella Swan as Hecate could be depicted as a very wise and mysterious figure. She may use her knowledge and powers to protect those around her. Just like Hecate is often associated with crossroads, Bella might be in a position to make important decisions for the characters in the story. She could also have the power to transform things or people, which is a characteristic often linked to Hecate.
Edward might be extremely protective. He already has a strong urge to keep Bella safe, but with the added connection to the Joker, he'd be on high alert. He might be worried about the Joker's influence on Bella and try to keep her away from that part of her life.
The Weasleys would probably be very welcoming to Bella. Molly would likely try to mother her just like she does with Harry. Ron might be a bit jealous at first, thinking Bella would steal some of Harry's attention. In the Twilight world, the Cullens would be cautious. Carlisle, being the rational one, would want to study this new connection between Bella and Harry. Edward might be a bit possessive over Bella still, but also curious about her new 'twin' and his world. Jacob would be confused and probably a bit angry, seeing yet another strange element in Bella's life.
In some fanfictions, Bella's character might become more confident. As an immortal, she no longer has the same fears of mortality. For example, she could be more fearless in facing dangerous situations.