Charles Bushman is a guy we only see briefly at the very beginning and very end of the movie. He's like the world's creepiest pair of bookends. We only know his name from the credits, so really, we just think of him as "that creepy killer guy," which doesn't even begin to fully cover the extent of his creepiness.
So, let's just talk about the elephant in the room right away: Charles is a man who has tied up women and killed them because he thinks they belong to him.
Charles is set up to show us a foil to Karl. Charles reminds us that the people in this mental hospital—Karl included—are there because they murdered people. However, Charles kills people because he feels entitled to, period. Karl kills people because he feels entitled to protect the people he cares about. So the question is: is there really a difference?
Karl killed because he felt it was the right thing to do. Charles kills because he wants to. He enjoys taking advantage of people, something he does simply by having a conversation with Karl.
CHARLES: I don't really like people who talk all the time. I like to do all the talking. That's why I think I'm so fond of you, 'cause you just so easygoing, you know. Although, I do sense a little tension in you, time to time.
Even in the mental hospital, Charles is searching for a victim.
At the end of the movie, Karl finally talks back to Charles, which shuts him right up, leaving Karl in peace.