In many Twilight fanfictions, the scenario of Edward saving Bella from Jacob can be quite intense. It often plays on the complex love triangle dynamic. Edward might save Bella from Jacob in a physical altercation, perhaps when Jacob's wolf instincts get out of control. This could be a way to reaffirm Edward's role as Bella's protector in the eyes of the fans who are rooting for their relationship.
One popular fanfiction could be 'Rescue in the Woods'. In this, Jacob discovers Edward's dark intentions towards Bella just in time and uses his werewolf strength to whisk her away to safety. Another might be 'The Saving Shift' where Jacob's wolf instincts lead him to Bella when Edward is about to do something irreversible. And there's also 'Jacob's Intervention' which focuses on Jacob's emotional journey as he decides to save Bella from what he believes is a dangerous relationship with Edward.
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.
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.
Edward might save Bella from Jacob when Jacob tries to force Bella into a life she's not ready for, like fully embracing the werewolf world. Edward, loving Bella as he does, would not stand for that and would rescue her.
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.
One great 'Edward Jacob Bella Fanfiction' is 'The Unforeseen Path'. It offers a unique take on the love triangle, exploring different character dynamics. The author delves deep into the emotions of the characters, making it a very engaging read.
I really like 'Forks' Newcomer'. In this fanfiction, it adds new elements to the story. The interactions between Edward, Bella, and Jacob are full of tension and unexpected twists. It keeps you hooked from the start as it plays with the existing dynamics in an interesting manner.
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.