It requires at least 25 hearts with Ori for her to become your girlfriend. If it fails, it resets to 0.
You can tell where you are with Ori by how the interaction window describes how she sees you. When you get the message "Ori is happy to see you!", you are at 20-25 hearts with her, so get 5 more hearts and then declare your love, and it should be successful!
I have plans on creating a wiki or guide to the game.