That's rotten luck. All I can really tell you is to bring more healing items and watch your health. The bookworm's attack stat is pretty low and the vampire status takes 1/5 of your total health at the end of each turn. She shouldn't b able to beat you on the third turn even at level 1 unless she managed to crit you, in which case, extremely bad luck since the enemy's crit rate is extremely low. I apologize if the beginning of the game is frustrating for you.
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.