Question:Is it okay for me to talk with a married woman from work to try and encourage her to come to services or help in her become a Christian?
Reason I ask is that I have been studying on and off with a lady from work. She is fairly young and has sinful problems she is going through (sex, lust and other things as well). She feels comfortable talking to me and I also feel the same. I am growing, I feel, by talking to her and giving her Scriptures to read. I am keeping it to email, text, and Facebook. We haven't met alone and I don't know that I will, but we have a gospel meeting coming up and I hope she comes. Am I in the wrong by this?
It appears you have a fairly good idea of the potential pitfalls. Everyone ought to hear the gospel, but you don't want to compromise the message by temptations to sin. Remember that it is false teachers who lure people through sensuality (II Peter 2:18-19). No Christian should want to give such an impression to another. When one or both people meeting have weaknesses, it is foolish to create situations where temptations in those weak areas can be acted upon. A person with an alcohol problem shouldn't be arranging meetings at a bar. A person who recently overcame a drug problem shouldn't be going to homeless shelters by himself. A person with poor sexual control shouldn't be meeting people of the opposite sex in private settings.
Solomon calls a young man he sees from a window naive because he walks through "the red-light district" in the evening (Proverbs 7:7-9). The young man was being stupid thinking he could come close to sin and not be lured in. In the same way, Christians need to treat sin as toxic waste. You never assume you are immune or that a moment's carelessness won't matter.
I was just reading some rules George DeHoff had for his life and I think was particular insightful: "I try never to say anything behind a man's back that would give me the least embarrassment to say to his face." That would be true for other situations as well. If your emails, texts, etc. with this woman were read by her husband, would it cause you any embarrassment or difficulties?
If you do get to talk to this woman face-to-face about the gospel, make sure to insist that her husband be present as well. Or ask an older woman or man from the congregation to come with you. Do invite her to services because others are present. Be care about offering rides; ask someone else to pick her up if she needs a way or have another person join you in the trip.
This is not to say I think you or she would give in to sin. I pointing out it is more sensible to make Satan's "job" as tough as you can possibly make it. Perhaps the easiest way to think about these things is always be conscious of needing to protect her reputation (whether she wants it protected or not), and then usually your reputation will be covered as well.