AFAIK it's not possible to add ID3 tags to M4A in Logic... or otherwise...?
But when you import your M4A into iTunes right-click and choose Get Info. Here you can set all the artist, album, etc options.
I believe this info is now stored in the file... at least it is on my Mac. Whether this info is transferred to another Mac or player I'm not completely sure.
Glad it's worked!
Just thinking of the easiest workflow and it's probably to tick the "Add to iTunes" in Logic's Bounce window and then locate the file in iTunes, Get Info and add the details you want to.
I used to keep music in aiff for iTunes... now, like you am either an M4A or Apple Lossless guy!