I remember in this episode it dealt with Bobby developing a liking towards Western outlaws on television; much to Mr. and Mrs. Brady's dislike.

Later on in the episode Bobby meets some old man who tells the story about how his father was killed by that particular outlaw. I can't remember what outlaw they were talking about. Was it Billy The Kidd, Jesse James... does anyone remember?

It was Jesse James.

Yup, Jesse James, and the episode was #89, "Bobby's Hero", from season 4 (not to be confused with the first season episode #21, "The Hero", which saw Peter save a girl from a falling shelf in Driscoll's Toy Store).