The bullets were more of a precautionary measure. If she was able to take Negi out sooner, he wouldn't have to fight Chao or vice versa. This would make Chao's plan proceed faster, as one of the main players would be removed from the scene.

Mana isn't just a mercenary. There must be something to explain what she's doing... Like someone must have killed her magister during one of their missions, and she wants to prevent the same thing from happening to other magister magi...