I think people are missing the point with Bill it isn't so much that she's googly eyed over the doctor, it's a huge inrush of guilt when she realises not only is he blind but he's blind because of her (or at least she'll see it that way).
She's an inexperienced person in a stressful situation feeling guilt because a man's about to die (and does she know/believe he's 2000 years old?).
And consider this, the Doctor foils the Monks' plan this time, but clearly they'll be back and who's gonna stop them if he's dead?
Don't get me wrong, I'm not saying Bill's decision completely made sense, just pointing out there was some rationales behind her making it.
Her not realising he's blind really does knock some IQ points off her however!!