the discussions are encouraged, but should always take place with respect and from an intellectual standpoint.. i don't know what to quote here.. but believe me, its out there..
instead of talking about Islam, why not ask her if there is anything truthfully and honestly she doubts about her own faith?
if say for examples, she doesn't understand Trinity, or Communion (if she practices this).. then tell her an Islamic stand point..
being preachy and over zealous puts you at risk for two things
1) turning her off completely to Islam (who knows.. maybe one day thru understanding and more complete knowledge, she will get Dawah)
2) by being preachy, you are put to a higher standard, but you are human... so any mistakes by you, can immediately be seen as a hypocrite by someone outside who will ultimately take that and run with it, if she is that kind of person....
so let the conversations be about faith, but don't be on teh corner on top of your soap box... be an example.
wasalaamu alaikum....