I don't get it - SPOILER ALERT
Why would having the bullet or hiding it from the police be in Elliot's advantage? Clearly the shot hit the books not the dead guy. We know that's not what killed him.
In the movie they seem to suggest the shot triggered his heart attack or whatever actually killed him but he had an existing heart condition. Anything could have triggered it like a car backfiring, the strain of the trip, or just the pressure from living a life of crime.
Elliot could claim the gun misfired when he was cleaning at some other time prior to or since that night. There's no test to prove when it was fired or who fired it. Besides, he was there the guy was there to commit and died in the commission of a crime. Of course Elliot might want to threaten or scare him in some way. A heated argument between the two could also have been a factor.
I enjoyed the movie but I just didn't get any of the bullet part of it.