In The Outsiders, why did Johnny want to turn himself in after the murder?

Johnny wants to turn himself in because he thinks he will get off easy.

Johnny and Pony go on the run because they are jumped by Socs and things turn deadly.  Bob was drowning Pony, and Johnny intervened.  At that point, they ran away because they were afraid no one would believe them.  Johnny has never been in trouble, but is worried that no one will believe his killing the Soc Bob in self-defense.

The boys go to Dally, and he helps them run away.  He tells them where to hide out and what to do.  When Dally comes to visit them at the church, he brings Pony a letter from Soda saying he is worried and wishes his brother would turn himself in.

I know Dally knows where you are, but you know him. He keeps his trap shut and won't tell me nothing. Darry hasn't got the slightest notion where you're at and it is nearly killing him. I wish you'd come back and turn your selfves in but I guess you can't since Johnny might get hurt. (Ch. 5) 

Soda understands why they went to Dally for help instead of telling Darry and Soda what was going on.  After all, Dallas has more experience with law-breaking and he did know what to do.  He got the boys out of town and in hiding, and served as a link between them and their families (well, Pony’s family at least). 

Johnny surprises Dallas by saying that he wants to turn himself in. 

"I got a good chance of bein' let off easy," Johnny said desperately, and I didn't know if it was Dally he was trying to convince or himself. "I ain't got no record with the fuzz and it was self-defense. Ponyboy and Cherry can testify to that. And I don't aim to stay in that church all my life." (Ch. 6) 

Dally agrees reluctantly.  He does not trust the legal system.  He understands that these two are not hardened criminals, however.  They are just two scared kids who got in over their heads.  

Johnny doesn’t get to turn himself in the way he planned.  Dally, Johnny, and Pony all get injured trying to rescue some kids who get caught in a fire at the church.  At the hospital, prison for Johnny is not really on anyone’s minds because he is dying.  Eventually, Pony is released and his legal troubles are much more minor.