One Big Player

Control your music while driving or biking without your readers. Easily select Artists, Albums, and Playlists.
You can figure out how to use it by playing with it for a minute or two. While not a CarPlay app, One Big Player is a good companion to CarPlay, keeping the tracks visible on your phone while the car's display shows a single song's details.
A great feature is Resume. When you re-open the app it picks up where you left off when you press Resume. If you had pressed the Shuffle before you closed the app, when you press Resume it will present the Album or Playlist tracks, perform a shuffle, and start playing.
One Big Player will only play offline (non-cloud based) music so be sure to download the songs you want and get them physically on your iPhone or iPad.