Yes, there might be. The 'Twilight' series has a large fanfiction community, and it's possible that someone has created a story where Edward leaves Bella and incorporated elements related to Artemis. However, it would take some searching through fanfiction platforms to find it for sure.
One possible plot could be that after Edward leaves, Bella is in a very dark place. However, she has always had an interest in Greek mythology, and one day she stumbles upon an ancient artifact related to Artemis. This draws the attention of Artemis herself. Artemis, seeing Bella's potential and her broken state, offers her a chance to start anew. Bella then embarks on a journey with Artemis, traveling through different realms, meeting other mythical creatures, and slowly finding herself again. Along the way, she may also encounter some vampires who are still interested in her because of her past with Edward, but with the help of Artemis, she is able to fend them off and prove that she is no longer the weak girl Edward left behind.
Bella may cope with Edward's abandonment by getting angry. Instead of just moping around, she could use her anger as a fuel. She might start to question Edward's motives more deeply. This could lead her to become more independent and less reliant on others for her happiness. She could also start writing in a journal, pouring out all her feelings, which would be a therapeutic way to deal with the pain.
It often starts with attraction. Edward is drawn to Bella's unique scent and her differentness. Bella, on the other hand, is intrigued by Edward's mysterious nature.
One common plot twist is that Edward's departure was actually a ruse to protect Bella from a greater danger. Maybe there's a powerful vampire or a group of them that he's trying to keep her away from, and leaving her seems like the only option at the time.
Well, in some fanfictions, Bella might be scared of Edward because of his vampiric nature. His superhuman strength and speed could be intimidating. Also, the unpredictability of his actions as a vampire who is constantly fighting his bloodlust could make Bella feel scared.
In some fanfiction, Edward might be mean to Bella to create drama. Writers may use this as a plot device to add tension to their relationship. For example, it could be due to some misunderstanding or an external threat that makes Edward act out of character and be mean.
One memorable moment could be their first dance in the fanfiction. It's a moment full of tension and unspoken feelings. The way Edward holds Bella gently, as if she's the most precious thing in the world, is really touching.
In this fanfiction, the relationship between Bella and Edward is turned on its head. Bella's role is now to shape Edward's character from a young age. Their interactions will be less about the intense passion of the original story and more about the tender, sometimes difficult, bond between a mother and son. She might worry about his future, his choices, and his safety in a way that is very different from the love - based concerns in the original narrative.
Their relationship develops as Edward imparts his knowledge to Bella. Since he's her master, he has a certain authority. But as time passes, Bella might start to question some of his decisions, which adds tension and also deepens their relationship as they work through these issues.