Wow, thanks for your discreetness!

The context provided by your subsequent post makes it clear I owe you an apology.
Please accept it.
There are some truths that you have given though I believe that the response you gave is a very good starting point, but sort of incomplete according to the question of the OP.
Sure, our example that we give with our lives is the most effective testimony that a non-believer can see. And your response is very good, and I would highly recommend it, but I have been in enough of these situations to know that 99% of the time once you give a response like that then they will take it to another level and test you and demand something a little deeper, which is the response that I gave. Because if you are not prepared to go deeper then you will be seen by that person as someone who has just taken a leap of blind faith, and that is a turn off. Many nonbelievers are willing to hear some spiritual depth of your Faith as long as it sounds logical, but if they think that you believe in something without knowing why you actually believe it, other than it just feels right to you, they won’t usually buy that.
I hope you can see this was precisely my reaction to your first suggestion. I realize your perspective must be that you felt you were giving the “why” for all the Church teachings and beliefs built on top of the propositions you suggested treated as axioms. Here lies our difference of perspective. What are axioms to you, are “a blind leap of faith…” to me - as well as to many others who are spiritually educated in multiple non-Christian spiritual traditions.
Plus, often times some people will have parts of the picture concerning the make up of the Bible, and it is just enough that they are confused and unsatisfied, and once they hear a clear response it can all fall in place for them and make sense to them. There has been a number of times that I have seen that light bulb go off in someones head after I have filled in some of the gaps that were missing. Then it is up to them to move on from there and decide if God’s Word is going to help them get closer to God or if they will continue to reject Him.
People sometimes need that clear cut answer about the make up of the Bible because there are so many mixed messages and wrong information about it from all the non-Catholics, such as the Apostles wrote the King James Version, King James wrote the Bible, etc etc. I have heard so many rediculous things like that that no wonder some people cannot trust the Bible, I wouldn’t!
OK, I see the appropriateness of your suggestions in these cases. I think they would apply more frequently to non-Catholic Christians than to non-Christians. I think this shows that one response is not going to handle all situations. You’re going to have to have the discernment to accurately assess the context of the interaction - something not easily done in response to a couple paragraph, out of social context, posts.