It's not true that she was totally cook when she entered the bath. She entered there panicking, being scared about what the hell happens to Ren (He took his time, and she was affraid he fell asleep). After that, she behaved in front normally though she felt like dying. Later she tried to convice herself she didn't and she's still pure. In the end, she decided regreting not seeing the whole so she will be able to make Ren's doll proparly. Totally not like her., but she's known for the fact she wants the dolls perfect (I remember it really good, cause I read millions times. There's nothing more fun that reading her Monologe out loud).
Sorry, I can't believe it will really work completely. Maybe for a little while, but if everthing is going to be solved just because of it... It's going to pathetic. All was needed is an act of stupid girl? come on, the writer has to put something more deep, otherwise it's meaning. And she still didn't really understood how Kuon's darkness started to rise, though she gives hints.