This is important to keep in mind, as farming FATEs is harder on certain classes, or should you wish to save up for any future classes that may come out. You could farm all 12 Atma using your Summoner, but then trade them in with your Bard's Zenith for the Atma bow instead.
Keep in mind that Atma are not specific to the weapon you collect them with either. Yes, after you've completed the quest once, so long as you have a Zenith weapon equipped, you can collect Atma from FATEs. I started out as a summoner and that was my first zenith, now I'm 50 bard with zenith, can I get Atma as bard even though I did the quest for it as summoner initially? If I started as a summoner can I get Atma if I'm bard zenith?