Traveler of the Moon (2003)

Blurb:
When most girls ask their parents for a pet they’ll get either a cat or a dog. In Yuh-ur’s case, she ended up with a bat and that’s not the end of it. Not only did she get a bat for a pet, it turns out that Dori is actually a vampire! Come and emerge yourself in an alternate world where magic is taught at high schools and vampires are a dangerous yet virtually extinct race. Traveler of the Moon intricately brings together a well told love comedy by narrating through the perspectives of various characters. And with all the varying personalities of the many characters in this series, every reader can fall in love with at least one aspect of the book.

Source: www.anisearch.com/manga/256