This is a very good question. My version of the story has a dedication to Bob Dylan, and I wondered why.
First, music is important to all teenagers. As Oates says in the story, music "made everything so good: the music was always in the background, like music at a church service; it was something to depend upon." Can't you picture where you were the first time you heard a certain song?
The program Connie is listening to, XYZ Sunday Jamboree, is a dedication show: "An' look here you girls at Napoleon's--Son and Charley want you to pay real close attention to this song coming up!" It was a way for people to send messages to each other. By listening to these dedications, Connie could imagine they were for her--the "trashy daydreams" her mother accuses her of having.
In answering your question, I just had to find out why she dedicated this story to Bob Dylan. In an interview, Oates said that Dylan's song "It's All Over Now, Baby Blue" happened to be playing while she was writing, which "struck Joyce as 'hauntingly elegiac,' similar in tone to the story she had written." Isn't it interesting that Arthur Friend calls Connie his "sweet little blue-eyed girl" at the end?