Do you mean when she became lost in Port Angeles? He drives her home because he took her to dinner after the 'attack' to make sure she was ok (and to spend some more time with her)...when she got lost in the woods..Sam brought her home. :)
Edward had, after he had been changed, a short time of, so called, 'puberty.' He didn't want to live on animalblood anymore. He wanted to hunt on human, like his nature is.
He only hunted on people who killed or raped. He thought, if I kill a murderer, it makes me less monstrous. In the end, he stopepd and returned to Carlisle and, then, Esmé.
Because of this, it was hard for him to just turn around and go away. He makes himself do that bye thinking of Bella and the fake humans they pretend to be. He tries to stay with Bella so he has no time to turn around and hunt the rapers down. Also, he alsready loves Bella so he wants to be with her.