In a large skillet over medium heat, brown the ground beef, onions, and bell peppers until the meat is no longer pink. Drain the fat from the pan.
If you'd like to continue this dip in a slow cooker, add the beef mixture, sloppy joe sauce, cream cheese, and cheddar cheese to a slow cooker set to low. Cover and cook on low for 2 hours or until cheese has melted. Stir before serving. Keep warm on the low or warm setting for serving.
If you'd like to continue on the stovetop, add the sloppy joe sauce, cream cheese, and cheddar cheese to the pan with the beef mixture. Turn heat to low and cook, stirring frequently, until the cheese has melted.
Serve immediately or transfer to a slow cooker set to low or warm.