When your mobile phone is connected to your car, the Bandcamp app should automatically show up in the Android Auto or Apple CarPlay menu:
Tap the Bandcamp app icon to launch the app. You’ll be able to browse through a selection of tracks and albums in your collection (items you’ve recently added, listen to the most, or have downloaded) as well as Bandcamp Radio. Tap on an item you want to play!
To avoid additional mobile data charges, you can also play items directly from your downloads tab.