Prerequisites: Complete A Floral Gift, give Rue a Moon Brooch
Unlocks: Dating with Rue
Rue is plainly impressed with your dedication to gardening, and her comments at the end of the previous quest hint at a strong connection between the two of you. If you want to take things to the next level you'll need to present a Moon Brooch to Rue. You can acquire Moon Brooches from Silky Stitch Tailor's, for the rather steep price of five Moon Cloves. Moon Cloves are rewarded to you by completing certain quests or healing patients, so if you don't have enough you'll either need to explore the town or knuckle down on working in the Clinic.
Take a Moon Brooch to Rue. She seems all too happy to take you up on your offer, and briefly considers traveling the world with you - before both of you realize that she needs to finish her schooling first. Still, a relationship is more than in the cards, and the quest will end with the two of you becoming a couple.