The song "She's a Mystery to Me" has a very usual history. Bono from U2 woke up with a tune in his head after listening to the soundtrack to David Lynch's Blue Velvet and thought it sounded like a Roy Orbison song. He played the song for the other members of U2, who agreed that it did indeed sound like a Roy Orbison song. While Bono was still working on the song, Roy Orbison met him backstage after a U2 concert and asked Bono if he would like to write a song with him.
Roy Orbison's final album, Mystery Girl, named for the song, was released in 1989 after his death. Mystery Girl shot up the Billboard Charts upon release. Traveling Wilburys Vol. 1 was already on the charts, making Roy Orbison the only other person besides Elvis Presley to ever have two simultaneous Top 5 albums on the Billboard Charts posthumously.
You can listen to Bono explain the process of writing "She's a Mystery to Me" in the clip and enjoy the Roy Orbison music video for the song.