Wow. I knew I'm unlucky, but I didn't expect to be that unlucky. Maybe you could add that inexperienced vampires can only use normal attacks the next turn after having successfully bitten Mila? Maybe they have to reload their teeth.
That wouldn't really make it easier, but would prevent two bites in a row, which is pretty frustrating.
And completely unrelated feedback: It's a bit confusing that second and third are capitalized in the books in the library.