You can't hide non-downloaded music completely but you can restrict it to only downloaded music by selecting that in the Music App. If it doesn't appear for you then edit the main menu, Playlists, Artists etc. one of the options will be Downloaded Music. This will only show downloaded music.
Thanks. That isn't what I was hoping for... I don't understand why they would remove this option. I have a lot of purchases that I have no desire to see or download to my phone.