You don't need to open the Music section of your iPhone's Settings menu to delete a playlist. The Music app on your iPhone running iOS 8.1 has the Delete option conveniently located on a playlist's screen. Instead of deleting an entire playlist, you can consider using the Clear option -- which removes only the playlist's content. You don't have to worry about accidentally deleting music during the removal process because deleting a playlist does not remove the playlist's songs from your iPhone's music library.
Tap the "Music" icon from your iPhone's Home screen to launch the Music app.
Tap the "Playlists" icon in the app's menu bar to open the Playlists screen.
Video of the Day
Scroll down the screen, if applicable, and select the playlist you want to delete.
Review the options to remove the playlist or the playlist's content. The Delete option removes the playlist and its content from your iPhone. The Clear option deletes all of the playlist's songs but leaves the playlist itself intact. If you choose the Clear option, you can then repopulate the playlist with new music.
Tap "Clear" and then select "Clear Playlist" from the pop-up menu to delete the playlist's content. You are then free to add new content to the playlist.
Tap "Delete" and then select the "Delete Playlist" option to remove the playlist from your list of playlists.