Well Fingers Crossed, good luck. I've been reading through the responses to your question...some have good advice, some not so good. I'm an evangelical who has been participating in a "bible study" with a JW for about 5 or 6 months now. Here's what you can expect:
1) Your study will most likely consist of the witness going through watchtower literature, which usually consists of one of the three: "What Does The Bible Teach?", "Awake", or "The Watchtower". The witness will then use proof texts from the bible to support the positions/claims of the literature. As one forum member here said, even if the witness doesn't use his/her literature, they will probably gravitate towards whatever material is being covered that month, because they don't study the bible per se, they study proof texts to support Watchtower theological positions.
2) Your witness will most likely use the New World Translation, as they believe that all other bible translations have been corrupted.
3) Your witness has been taught that all churches and christian organizations outside of the Watchtower are part of Babylon, and therefore you are not a true believer and are apostate.
4) Witnesses generally don't conduct studies alone, so there may be another person present (although if a witness feels comfortable around you they may conduct a study alone).
First a warning: I would only recommend a study for those who are mature Christians and grounded in the Word of God. Of course since the reason for the study in the first place is because of a romantic involvement, I'm sure my advice will be quickly discarded
With that being said, a study with a witness can be a rewarding experience. One of the things it will do is force you to re-examine your beliefs and the scriptural basis for those beliefs. You might also discover that despite the demonization of the Watchtower organization by evanglical Christianity, witnesses are actually people!
Finally, I would say that if you are going to participate in a study with a witness, be kind and courteous. Remember 2Timothy 2:24-26..."And the Lord's servant must not be quarrelsome but kind to everyone, able to teach, patiently enduring evil, correcting his opponents with gentleness. God may perhaps grant them repentance leading to a knowledge of the truth, and they may come to their senses and escape from the snare of the devil, after being captured by him to do his will."
Also remember that Paul became all things to all people so that by all means he might save some. To those who were jews, he became as a jew. To those under the law, he became as one under the law. So to a witness, why not become as a witness? Pray to Jehovah God if you are leading prayer. Quote scripture from the NWT whenever possible. If your study involves the use of Watchtower literature, be sure to familiarize yourself with the literature beforehand.
In closing, I don't know exactly what your motivations are for participating in this study. If in fact part of the reason is romantic, this may not end well for either of you. I can't stress enough that this should only be undertaken by those who are mature christians who will not be blown about by every wind of doctrine. JW's are very good at what they do, and they can chew up and spit out your average christian (who is largely ignorant of what is in their bible).
That being said, providence to you! May God grant you wisdom and discernment, and may God bless your study and open the eyes of the blind!