Can I transfer my Apple Music membership from my iPhone to my iPod.

Hey Splashcat,
I understand that you would like to get the music from Apple Music to your iPod. This is something that you can do and you would just do that with iTunes. Just follow the steps like you have done in the past on syncing music to your iPod. I would make sure that you have downloaded the tracks in iTunes so that you have something to sync over. Take a look at the article below for more details on syncing over
Add music from the Apple Music catalog to your library on your iPhone, iPad, iPod touch, Mac, or PC
https://support.apple.com/en-us/HT204839​
Sync your iPhone, iPad, or iPod touch with iTunes using USB
https://support.apple.com/en-us/HT201253
Take care