Perhaps in the fanfic, there's a task or a mission that requires knowledge of Bulgarian. For example, if they are searching for a magical artifact that has some connection to Bulgaria. Hermione, being the resourceful one, would have learned Bulgarian in advance to help with the search. It could also be that she wants to expand her magical research and Bulgarian magic has some unique aspects that she can only access through understanding the language.
One reason could be her thirst for knowledge. Hermione is known for her love of learning, so she might have decided to learn Bulgarian just for the sake of it. Another reason could be related to a relationship, like with Viktor Krum, which gives her an incentive to learn his native language.
In the fanfic world, Hermione might speak Bulgarian to gain an advantage in the wizarding community. Since Bulgaria has its own magical traditions and spells, speaking the language could give her access to new spells or magical techniques. Also, it could be a way for her to stand out among her peers and show off her extraordinary language - learning abilities.
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