You must be level 40 to get the Triage quest, as well as reached 220 FA, if I recall.
And this quest is most easily done with your nameplates up, and someone else doing the quest with you.
The only problem is that the person has to be eligible for the quest, or they can't assist in "healing" the mobs.
After that, you garner all of your further types of bandages from this same trainer, as you reach certain points, you'll be able to raise.
It goes, Mageweave, Heavy Mageweave, Runecloth, Heavy Runecloth.
