You don't have to make a new character. You need a Level 30 Archer and a Level 15 Pugilist to be able to unlock the Bard. What I would do is keep leveling your Pugilist and following the story quests, until you receive the airship pass. This will eventually take you straight to Gridania where you can then multiclass as an Archer. Once you reach Level 30 as an Archer, you'll eventually stumble on the quest that will unlock Bard.