after saving bella when she became lost why does edward decide to drive her home?

Do tu mean when she became lost in Port Angeles? He drives her inicial because he took her to cena after the 'attack' to make sure she was ok (and to spend some más time with her)...when she got lost in the woods..Sam brought her home. :)

So he wouldn't go back and kill the guys that followed Bella

so he dosent kill the guys and to make sur is o.k because he cares:)

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 o 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.

She had no other way inicial because her friends where already back at forks