It’s great that you’re keen to look to the Bible for advice when thinking about relationships.
I think a great place to start is to look at what the Bible says about marriage. Although it might seem like marriage is a long, long way away, the aim of Christian dating is to find a Christian partner and so the dating relationship is to be modeled on the marriage relationship. Although marriage might not seem like an option in the short term, intimate (boy-girl) relationships should always hold open the possibility that it might result in marriage.
With that in mind, here are some passages that might help you think through your relationship:
1 Corinthians 7:39
Most women in the first century didn’t have choice about whom they could marry. The one exception was a widow - she had complete choice. Paul tells he she can marry whomever she wishes - as long as they’re a Christian (the way he puts it is someone ‘in the Lord’). So make sure that the person you go out with is someone who is also a Christian.
1 Corinthians 7:8-9
Christians are free to marry or not to marry. There is nothing wrong with going out with someone or not. So don’t feel any pressure that you ‘need’ to have a relationship or take your relationship any further. Staying as you are is perfectly fine. But having said, that, that doesn’t mean you’ve done the wrong thing if you start going out with someone.
Wives are to submit to their husbands. Husbands are to love their wives and lay down their lives for them. So if you’re a girl, make sure you go out with someone that you respect, that you will be able to submit to - someone who will lay down their life for you. And if you’re a guy, make sure you go out with someone that you’re prepared to lay down your life for, and who will respect you and be willing to follow your lead in the relationship.
1 Thessalonians 4:3-8
One area that is often a stumbling block for people going out is falling into sexual temptation. So it’s important to make sure you both are committed to living in a way that is going to help each other in this area. Have a look at How do I avoid doing the wrong thing in a christian relationship?
These a just a few parts of the Bible that might help you in your situation.
Can I encourage you also to find an older Christian that you trust to talk about it? Dating is a complex issue, and it can be really helpful to have someone to talk to about it - not only before you start going out with someone, but when you’re going out with someone as well. Please feel free to ask more questions if you would like to follow up anything mentioned here!