Due to Apple’s DRM policy you cannot move your videos from iTunes app to your iBridge Air using your iOS device
But there is a solution, though.
The simplest way to transfer your movies 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 movies you want to transfer and drag and drop them to your iBridge Air. But please note that if your video file is DRM protected, you will not be able to play it on your iBridge Air even if you succeed in moving it.