Hey, thanks for playing! So there are basically relationship "tiers" for the girls. Once your relationship moves up two "tiers" you'll be able to ask someone out for a date. You need to get to the next tier after that to ask to the dance. You'll know when you've moved up a tier because the girl will start acting more friendly toward you when you talk to them.
The reason the system is like that is that we wanted to have a more realistic sense of when the right time to ask someone out is, rather than just the game telling you when you're allowed.