Levels 1-125 - Learn bandages from a First Aid trainer, up to Silk Bandages.
Levels 126-180 - Purchase all three books from Deneb Walker in Stromgarde and read the Expert First Aid book to train past 126 and keep making Silk Bandages to level.
Levels 181-210 - Read the Heavy Silk Bandages book and use them to train up to 210.
Levels 210-225 - Read the Mageweave Bandages manual and use them to train up to 225.
Levels 226-260 - Get the quest from the First Aid trainer in IF who sends you to the Surgeon in Theramore (for Alliance) to gain Artisan status and learn Heavy Mageweave Bandages.
Levels 260-290 - Runecloth Bandages, learned from the Surgeon.
Levels 290-300 - Heavy Runecloth Bandages, also learned from the Surgeon.