Well, that could lead to all sorts of intense and unexpected plot twists. Maybe it would force the other characters to take drastic actions to rescue her.
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.
Some fanfictions focus on the time when Bella was separated from Edward in 'New Moon'. They might explore what Bella was really thinking and feeling during that time more deeply. It could show her inner struggle and how she coped with the loss in ways that the original story didn't fully cover.
Another direction could be that they focus on building a normal life within the vampire world. They might start a school for other vampires or hybrids, teaching them how to co - exist with humans. Edward could use his knowledge of music and literature, and Bella could share her experiences of being human - turned - vampire.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions, and you can easily search for Bella and Edward New Moon ones by using the relevant tags.
She might first be in shock. Then, she could turn to her friends like Jacob for support. Jacob, being protective, would likely try to help her in any way he can, whether it's providing for her basic needs or just being there to listen to her fears and concerns.
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.
In some fanfictions, their relationship deepens on a spiritual level. Since they've both been through so much, they start to understand each other's souls better. They communicate without words, and their love becomes more of a profound connection that goes beyond the physical and emotional aspects.
The Volturi also keep an eye on this situation. With Bella not forgiving Edward, there is instability in the relationship between the Cullens and Bella. The Volturi are always looking for any excuse to interfere in the Cullens' affairs. This unforgiving state of Bella could potentially give them a reason to step in, which would endanger not only Bella and the Cullens but also other characters who are associated with them.
The Cullen family's reputation could be affected. They are supposed to be a family with certain values. Edward leaving Bella in such a situation could make other vampires view them in a negative light. Also, Edward himself might face internal conflict. He loves Bella but leaving her pregnant goes against his sense of responsibility.