Hmm. I was going to say to tell her the truth about what you know, but I see that you want to fade because of your family, so that will be bad for you if she goes and tells the Elders... bad situation. I guess it is in your best interest to keep doing what you are doing. Ask questions and such, but don't commit. Maybe say you are concerned / doubtful but never really commit to anything. That way she can't say too much to the Elders. The Elders will just think that you are weak if she does tell.
I would suggest to STICK TO THE BASICS with her. Other questions are okay, but make sure the focus is on the basics. What I mean by that is sticking to the outer rim. Focus on questions like, Why do you think this is the truth? Whatever she says, question that. A lot will say it's because JWs seem to follow the Bible more than any other religion. (like preaching) Make sure you study up on the JWFacts.com website. Escpecially the "preaching" article, as it debunks everything the WTS uses to support that claim. If she understands that, then she will start to question. She may say, "What about this?" Answer that. Debunk that teaching, whatever she brings up. Debunk it. She will eventually have nothing to stand on. You say she is new, so she might not be able to cite things from the top of her head. Be considerate and ask the question yourself if she is pausing trying to think. If she needs time, tell her that whenever she has a question she can look it up or ask you and you guys can research it together. Try not to be authoritive on the matter. People don't like it when you tell them what to do. Why do you think the Society always tells you to direct people to the book and don't talk from your head? So instead of doing the above from the top of your head, offer to research this with her, and say it in a way like you are partners. "We can research the WTS together." This way, it will be hard for both of you to come away with different ideas. You should all agree on what is the truth and what isn't. If the conversation gets sidetracked, make sure to focus it back to the basics before too long.
If you get stuck on a subject what the JWs seem to have ground (this can happen, because the Bible is really open to interpretation), you can move on to another subject, but if that sticks with her and she keeps coming back to it as grounds to belive the WTS, it may be time to just set her straight on the Bible itself. I seriously doubt you will have problems reasoning with an intelligent person about the lack of evidence that the Bible is God's word. It's just not something you can argue against, if you do it right. (this is a reply to Morbidzbaby's reply, also) Either the person realizes the truth or they get a case of cognitive dissonance. Simple as that. You wouldn't want to be in a relationship with a person like that, anyway, is my guess. With the Bible, begin with the around the rim questions, again. Just the basics. "Why do you believe the Bible is the inspiried word of God?" Again, make sure it doesn't get sidtracked from the mainpoint. Sometimes people can bring up a side teaching you can't argue against that well. Even though they often don't do it intentionally, don't fall for it. Stick with the main points, as when those fall, everything falls with it. For instance, don't talk about whether Jesus existed or not. That's irrelevant. Even if he did exist, when the main points are argued against, there will be no reason to believe he was God's son, God, or anything else. Or even if he was (hypothetically, here), we already know the Bible isn't God's word therefore it is not HIS word. So talking about subjects like that is pointless. Stick to the outer rim.
IMO, the outcome of atheism is a lot better when it comes to the real truth. When fighting the JW religion, you may be using arguements from another religion, which is biased themselves, and can be open for rebuttal. When argueing against the Bible, there really is no ground to stand on. On the other hand, coming to terms that the Bible is not true can be a harder thing to grasp for some people, especially if they grew up religious. That's why you see many ex-JWs who still believe in the Bible, even though it's just as wrong as the JW religion. Sometimes the best step is to get them to realize the JW religion is false and then get them onto the topic of the Bible's inspiration.
Anyway, stick with the basic questions of the Bible and research them online. Get started with the Reddit Atheism FAQ if you haven't read it already. I wish I had learned about it earlier myself: http://www.reddit.com/r/atheism/faq
If you get stuck on something, ask someone on a science forum like SciForums (in the religion section). They helped me when I was researching whether the Bible was true. You can look up my thread if you want, but it is quite long: "A challenge to atheists" (not the one labeled #2) It may seem bias, but no one is saying to accept their word as truth. Reason on what they counter and see if it makes sense (it will). If you have to, you can look it up. Now do the same thing with her.
If you decide to go the Bible route, here is a silver bullet contradiction that has to legitimate rebuttals as far as I know:
According to the gospels of Matthew and Luke, Jesus was born during the reign of Herod the Great. But Luke also wrote that Joseph and Mary had to go to Bethlehem for a census by Quirinius while she was still pregnant, and this event has been dated at 6 A.D., or ten years after Herod the Great died in 4 B.C. There have been no historical records to indicate that any Roman census was held prior to 6 A.D.
Either Matthew is wrong, or Luke is wrong. Or more likely, both are wrong, rofl. I fail to see how something inspired of God could make a mistake (and of course this is not the only one) like that. An inspired book should be infallible, no matter WHO it was written by. It could be written by turtles for all I care, as long as it's infallible. But the Bible is not, it is far from that.
In my research, I haven't found a commentary that covers this.
As I've said before, I was raised a Christian myself, but after diligent research and debate I couldn't continue to be oblivious to the lack of evidence that the Bible is indeed inspired of God. In fact, it seems the Isrealites and Christians borrowed from other religions, such as the Sumerians and Egyptians. I wouldn't want to have cognitive dissonance. Believing in something you know is wrong is against my personal principles, no matter how much you tell yourself it is right. I would rather die than have cognitive dissonance.
Hopefully this helps!