*note: you didnt say you were asking a christian girl out.... however if you are asking for yourself i would imagine you would probably not be asking a girl out who wasn't. based on the idea that you're asking for yourself.....................
from my observations i've come to the conclusion if you're looking to date a legit christian girl it might be better to approach her as a friend and her to know her first. i'm not really friends with alot of christian girls, but from the few i know, i've found they would prefer knowing the guy at least a little bit before being asked out. I've noticed that of my christian guy friends they have had much more success in getting date with a christian girl when they knew her first.
my opinion on christian girls an this topic is kind of skewed though. I think about 85% of them have unrealistic expecations for what they want in a guy and how they want to be courted. Which makes it frustrating to be a guy in this situation. But then again I think 85% of christian guys are gutless push overs, which only makes a dating situation less likely to succeed.
Considering I wouldn't claim to be a conventional christian women, I have always prefered a guy come straight out and be like "hey i wanna take you out". My current boyfriend and I didn't really know each other all when we first started dating. We talked once and really hit it off so he asked me out.