Bella comes to the conclusion that Edward is a vampire right around page 138-139. She realizes the truth but doesn't quite fully admit it to herself yet. When she realizes that he is a vampire, she thinks about two options: the first option is that she could tell him to leave her alone, run away from him, refuse to see him, and never talk to him again. The second option is to continue to act as she had been, to see him, to talk to him, to be with him, and accept him. She thinks that if he were going to hurt her, he would have done it already, and she believes that he is good. She makes her decision rather easily, because she is already falling in love with him. She really can't stay away.
When she tells him she knows, she explains how she heard the story from Jacob Black, and he freezes, only barely hiding his nervousness. She tells him, "I decided it didn't matter." This happens in chapter 9, on page 184 of my edition. When this happens, the truth is out in the open, and she makes it clear to Edward that she trusts him and is willing to work things out to be near him, even though he believes this is wrong. Neither of them can bring themselves to stay away from each other.