Are you just trying to listen to your purchases? First, create a free fan account. Then, use the Bandcamp iOS App to play all your purchases. You'll be able to listen immediately without having to go through a computer first. You can also stream your purchases via Chromecast and Apple CarPlay when you’re on the go!
Are you trying to download a copy of your purchase to your device without using a computer? Unfortunately, Apple doesn’t allow direct music downloads to iOS devices like iPhones or iPads.
If you want your music in your native Music app, you'll need to download it to a computer and then sync it to your device.