I really do not believe that Billie knows what happened to her daughter and hope I am not proved wrong. As far as checking on her in the bed, I don't even believe she did this, I think she said she did because NG was asking her in such a way, she felt she had to say it, and that is why her answer was so awkward.
I think Billie's defensive attitude comes from her disbelief that SA is being called a suspect, when she can't see a reason for it, and from the fact that some people actually choose to believe the affadavits over her.
I think she has made a big mistake in refusing to deal with ktxs or singling out any media she won't talk to anymore. That kind of action generally leads to the digging up and printing any other little bits of dirt that may have yet to be uncovered. It also makes her appear to be more interested in what the media is saying that makes her look bad than in finding Hailey.