Actually, there is a way.
You just have to wear clothes, that make a specific sound.
You know - when you finish dressing up and you look at yourself afterwards and it makes a sound?
Well, if it makes this sound then the woman will like it, and she'll give you the Bamboo Sprig Hat!
Plus, the Bamboo Sprig Hat also has it's own unique sound to it. It's scared me when I first heard it... um... xD
Hope I helped. :)