OP - you handled that situation with grace, respect to you for that.
In terms of "giving an answer", this involves knowing your own religion (which I'm sure you do), but also knowing their religion and (unfortunately) poking holes in it.
Studying a philosophy/religion/spiritual path with the sole intention of finding its faults is a fruitless waist of time and gives you no peace. However, studying with the intention to find similarities and understand differences gives a greater reward (speaking from experience).
The thing about giving someone like that an answer is you first need to know what denomination of christianity she follows. If she's one of the outliers (LDS, 7th day Adventist etc.) then it's easy to put her down. But if she's a hardcore Baptist (or even a Methodist), then it requires more homework on your part ("knowing your Bible", so to speak). And from what you've described, chances are she's a Baptist.
Ultimately, it will end the same way i.e. neither of you will change your faith. But with a little homework, the next time something like this happens, you'll be ready with an answer or two (if needed).