Jgnat makes an excellent suggestion. Since you are a Christian you have a deep appreciation for the power of God's word.
I can't tell you enough how fruitful Bible studies with a JW can be.
A big key to this is the fact that you and your wife have a different, and due to JW toxicity, competing faiths. THe first thing you want to do is adopt an extremely humble attitude. Consistently be honest (accomodate new facts and ideas that contradict your paradigm) and honor truth wherever it is found. WHEREVER. Truth is truth. Find truth, you are looking at God.
Going along with the above advice is your overall method. The best way to teach is to ask questions. Then the person owns their thoughts. I would spend some time breaking the book to be studied into sections if 4 verses and no bigger then 8. Sometimes a topic will cover much more then that. Break it up over several studies. Spend some time before each study reading orthodox commentary. If you are not familiar with jw orthodoxy, you can read their take from... is it All Scriptures Inspired? I think so.
Next, as you study the Bible with a JW, there is a running theme you will want to keep an eye out for. The JW as you noticed ignore Jesus. They want to be the mediator between men and Jehovah. Furthermore, they relegate him to the secondary status of a created angel. As you read through John, ask questions about why Jesus is referred to in this way or that. Continue to point out the glory and honor bestowed on him. Such reverence is only appropriate for a Diety. Even if you wouldn't go that far, the jw has to realize that Jesus is more then their religion makes out.
Feel free to post questions here to "know how a dub will answer".
Have these studies as often as you can. You are a tether, a link to the outside of her insular world. The jw will want to focus on the "what" of faith rather than the "how". You can keep the peace by emphasizing the how. Humility, honesty, sound reasoning, openess to new ideas. All these things are more important than particular facts. Because if how you go about discovering your faith is sound, then ultimately your faith will be the most factually correct as well.
CYP