As you might already know, Apple has a very strict DRM policy. As a result, Music and Videos apps on iOS do not support exporting data to another apps or external devices.
But there is a solution, though.
The simplest way to transfer your music library to your iBridge Air is to use your Windows computer or macOS computer. Launch iTunes on computer, connect your iBridge Air using the cable it came with, choose music (albums, playlists) you want to transfer and drag and drop it to your iBridge Air.
But please note that if your audio file is DRM protected you will not be able to play it on your iBridge Air even if you succeed in moving it.
You can also create folders on your iBridge Air to organize your content. When plugged in a computer, it works like an ordinary flash drive.