Honestly? Even leaving aside what the bible has to say about it, I think that if you consider the bible so important, and the person you date doesn't, you'd probably both be better off finding someone else. Think about it - if she's not a Christian and you act as a missionary, she's liable going to be irritated with your proselytizing. If she's not a Christian and you don't proselytize, how will things go when you're deep into the relationship and she starts taking issue with you wanting to teach your children about Christ? Regardless of how this goes, it's going to be a rocky road.
Personally, I wouldn't date a "serious" Christian. A Christmas-Easter Christian, sure (my current girlfriend was, until she realized that she didn't really believe), so long as they accepted that I am an atheist and intend to raise my children to think critically and understand science, but a Christian who wonders what the bible has to say about every action in their life? Never. It would be a disaster. And the reverse is just as true. Nobody would enjoy that.
...Granted, that's not very biblical, but you really should think about this not just in terms of "what does the bible say" but also "what is going to lead to a good relationship". The bible, despite the claims of some here, does not contain all the answers on everything. Some things, like a good apple pie or a good relationship, aren't really held within its pages.