In some plotlines, it could be that Bella has made a deal with Peter in order to escape Edward's over - possessive nature. Peter might have his own reasons for wanting to get involved, like a long - standing feud with Edward's family. So, he uses his wits and resources to whisk Bella away to a place where Edward can't find her. This could lead to a whole new adventure for Bella as she adjusts to life away from Edward and with Peter's protection.
She might be in shock at first. After all, she was in a life - threatening situation. But then she could feel extremely grateful towards Edward and their relationship might grow stronger.
Bella would likely be very frightened during the car incident. Once Edward saves her, she'd be extremely relieved and probably feel even more attached to him. Edward, on the other hand, would be initially worried and focused on getting Bella to safety. After saving her, he might feel a sense of relief as well, but also a bit of that over - protective feeling that he often has for Bella.
One possible reason could be that Edward believes Charlie is a threat to Bella in some way that Charlie doesn't realize himself. Maybe Charlie unknowingly gets involved with some dangerous elements, and Edward, with his vampire senses, detects it.
There are quite a few out there. You can start by checking some popular fanfiction websites like FanFiction.net or Archive of Our Own. Just type in 'Peter Saves Bella from Edward' in their search bars and browse through the results. Some might be really creative and offer unique takes on the scenario.
One possible scenario could be that Bella is out alone at night and a group of drunk guys start harassing her. Edward, with his vampire speed and strength, appears out of nowhere and scares the drunk guys away. He then takes Bella to a safe place, like his house or a quiet café.
In some fanfictions, Peter might be captured by an enemy who wants to use his spider - powers for evil. Wade discovers this and embarks on a rescue mission. Along the way, he might team up with some of Peter's friends or allies, like MJ or Ned. The story could also involve Wade having to face some of his own inner demons while trying to save Peter. For instance, his past experiences might make him hesitant at certain points, but his determination to save Peter overcomes those hesitations. And of course, there would be some great action scenes and witty dialogue between the characters.
In many such fanfictions, Edward might use his superhuman speed to reach Bella just in time. He could have sensed her danger through his vampire instincts and dashed to the cliff edge, grabbing her before she falls.
One possible plotline could be Bella coming from a less - privileged background and Edward, being wealthy, takes her under his wing financially. He could buy her nice things, like expensive clothes and jewelry, while they also develop a romantic relationship.
One possible plotline could be Bella initially resenting Edward as her step - dad but then gradually coming to understand him better and they form a unique bond. Another could be Edward struggling with his new role and having to deal with his own feelings for Bella in a more platonic way than in the original story.
Edward could use his mind - reading ability. He reads Charlie's intentions and plans his moves accordingly. If Charlie is about to make a decision that Edward believes will be bad for Bella, he can intervene at the right time. He might also be able to manipulate the situation subtly so that Charlie changes his mind without realizing it.