So, first off, the Bible doesn't directly say anything about whether it's ok to date non-Christians. In fact, it doesn't even say anything directly about dating. (That's because modern dating didn't really exist back then like it does now). That means we need to look for some general principles that can help us make a decision, rather than direct teaching about it. So, I can think of something from the Old Testament and something from the New Testament...
Old Testament Example
How familiar are you with King Solomon? He was David's son and one of the richest and wisest kings of Israel (from 1 Kings 1-12). However, he also had a weakness for women. (He had 1,000 wives and concubines). And even though God strictly told the Israelites not to marry foreigners, Solomon married many foreign women. You can pretty much guess that happened. The foreign, non-Jewish women turned Solomon away from God and he started to build temples to their Gods and did evil in the eyes of the Lord.
I would encourage you to read the story; it's actually kinda sad to read how Solomon fell. This part of the story is in 1 Kings 11:1-13. Here's the lesson that we can learn from it. It comes from the Lord's command to the Israelites: "You must not intermarry with them, because they will surely turn your hearts after their gods" (11:2). When we connect ourselves deeply with a person who does not share our faith or commitment to God, the relationship has a tendency to draw us away from Him. I've certainly seen that happen many times. Yes, sometimes the boyfriend/girlfriend becomes a Christian, but those stories seem to be few and far between. This is because when a guy and girl date, they begin to develop common values and behaviors. It usually tends to shift towards the stronger (or more demanding/controlling) personality, and in most Hmong relationships that seems to be the guy.
New Testament Example
In 2 Corinthians, one of the major themes that Paul talks about is rejecting false teachers. As part of this warning, he offers the following command, "Do not be yoked together with unbelievers." (6:14). That was the NIV. The New Living Translation (NLT), writes it like this, "You are not the same as those who do not believe. So do not join yourselves to them." This is probably the most common verse that Christians quote when it comes to dating or marrying non-Christians. Like the story of Solomon, although it's not directly talking about dating, there are some principles that we can pull out to help us.
I would encourage you to read the whole section (2 Cor. 6:14-7:1). It has some pretty powerful imagery and contrasts.
So, what can we learn from this passage? First off, there is a mismatch when we pair ourselves with a non-believer. This idea of being "unequally yoked" is a reference to the Mosaic Law that said you shouldn't tie up an ox (a strong animal) with a donkey (a weak animal) to pull the same plow (Deut. 22:10). If you did that, they wouldn't be able to work together and they probably would end up doing more harm than good. I think the same thing can happen in a relationship between a Christian and a non-Christian. They each have different guidelines/morals on which they make decisions, so they would most likely clash. For example, one person might think its okay to lie to parents about where they're going, but the other person might not think its okay. I've also seen this when it comes to making decisions about how sexually active to be. The non-Christian might think it's totally fine to have sex and the Christian might not. Or in situations where they are sexually involved, the Christian might feel strong guilt and shame about it and want to try to stop, and the non-Christian might not understand why it's such a big deal.
So, the issue isn't an us-vs.-them: Christians are good, non-Christians are bad. In fact, that kind of thinking is prideful and hurtful. The real issue is having different value systems and the inevitable conflicts that would arise because of it. This principle isn't just restricted to Christians and non-Christians. For example, if an ultra-conservative Republican wanted to date an ultra-liberal Democrat, I would probably recommend against it because they would get into too many arguments. Their value systems and political ideologies are just too different. Believe it or not but this can even apply to two Christians. If one was a strong Christian and the other was a really lax, non-committed Christian, they wouldn't make a good pair. In fact, with Pang Foua and I got engaged back in college some of our friends were concerned because she was so much stronger of a Christian than I was. To them, it was a case of being unequally yoked. (Thanks be to God that he was able to help an immature guy like me grow up a bit in Him and in myself.)