Just trying to listen to your purchases? Create a fan account (they’re free!), then use the Bandcamp iOS App to play all your purchases immediately without having to go through a computer first. You can also stream your purchases via Chromecast and via Apple CarPlay when you’re on the go!
Trying to download a copy of your purchase directly to your device? Unfortunately, Apple doesn’t allow direct downloading of music to iOS devices like iPhones or iPads.
If you want your music in your native Music app, what you can do instead is download your music to a computer (there any format is fine) and then sync to your device.