John Piper gives some Biblical counsel about physical affection before marriage.
The Bible does not have a section of rules for engaged or dating couples to follow, but we can look at Biblical principles apply specifically to this. The Bible does celebrate sex as a gift for husbands and wives to enjoy. Just look at the Song of Solomon, or Proverbs 5:18,19. In 1 Corinthians 7, Paul confronts the false teaching that it's more spiritual to avoid sex, affirming that sex is a great thing and it's a part of intimacy, not something you just have to get through in order to have a child! But it is only for marriage. In 1 Corinthians 7:9 he has direction for those who are unmarried but sexually awakened: But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion.
John Piper points out that our bodies were designed by God to respond to sexual touching with a desire for sexual intercourse. If you're not yet married, don’t do things that awakens your passion to go further. Have a conversation that establishes boundaries, committing yourselves to stay away from the kind of privacy and touching and kissing that would take you down that road.
Men, be strong here. Set a pure and holy pattern for your relationship today. Don’t make your girlfriend or fiancée be one to put on the brakes. Women, don’t entice a man to touch you or try to see how far he'll go. And if you tell him "no," ahead of time or in the moment, you will learn a lot about his character through his response.
John Piper's final point was to those who are not in a relationship. If you are not married, you are not any less of a person. Jesus was not married, did not experience sex, and he was a prefect and whole human being.