Instead of calling it extra hearts, why not label it as 'Body Armor' or if you really want to con the idea on it, name it 'Baddy Armor'. I can see why extra hearts would be really confusing to players, however, it's inevitable that it will be mistaken for actual health, but they'll learn to catch on regardless.

My personal suggestion would be that you can obtain Baddy Armor from armory stalls (where else would someone get them?), but for starters, you may only have one additional bar. Through questing, you unlock the ability to obtain more hearts, thus allowing you to take on more rigorous quests (not necessarily requiring a certain amount of hearts to enter, yet implying the benefits). After you lose it, you can easily buy more, or have a slight chance of getting it through an enemy drop, and like Twillit said, it should correspond to AP. Higher AP = More drops, such as bombs and arrows.