From HP COS, and related to this question:
“Oh, it’s you,” she said when she saw Harry. “What do you want this time?”
“To ask you how you died,” said Harry.
Myrtle’s whole aspect changed at once. She looked as though she had never been asked such a flattering question.
“Ooooh, it was dreadful,” she said with relish. “It happened right in here. I died in this very stall. I remember it so well. I’d hid- den because Olive Hornby was teasing me about my glasses. The door was locked, and I was crying, and then I heard somebody come in. They said something funny. A different language, I think it must have been. Anyway, what really got me was that it was a boy speaking. So I unlocked the door, to tell him to go and use his own toilet, and then —” Myrtle swelled importantly, her face shining. “I died.”
“How?” said Harry.
“No idea,” said Myrtle in hushed tones. “I just remember seeing a pair of great, big, yellow eyes. My whole body sort of seized up, and then I was floating away. . . .”
So basically she saw the eyes, died, and then turned into a ghost. But how was it that she didn't see the basilisk after her death, or even got petrified à la nearly headless Nick?
Edit: I 'm asking on why she doesn't remember seeing the basilisk after she dies. If someone has a good reason to think that she didn't become a ghost immediately so that the basilisk had time to go somewhere else, it would nice to have some references to support it (I found none). Or maybe the basilisk evaporated after killing her.