As you can see in the screenshot above, it seems that trying to transfer songs you’ve saved from Apple Music to the iPod nano or shuffle will result in that error message. It does not appear to be a bug or a glitch, and according to 9to5Mac’s sources, it seems that this was done on purpose to prevent piracy.
Basically because the iPod nano and shuffle don’t have access to WiFi and other online services, Apple is unable to authenticate whether or not the device has an active Apple Music subscription, unlike iOS devices like the iPod touch, iPhone, and iPad. This means that if Apple were to allow Apple Music on the iPod nano and shuffle, users could download any song they want within the 3 month trial, save it on their iPods, and cancel their subscription.
That being said we’re not sure if this will be a permanent limitation, or if Apple will somehow come up with a way to accommodate iPod nano and shuffle owners in the future, but for now that’s the way things are.