Whooo, wait....your description sounds pretty specific to me. Just in case there's some sense of urgency here, I will give it a try, but this is a real challenge. The problem with Asian shows is that it's usually the guy who doesn't take dating seriously.
Lucky Romance The female lead is eager to have sex with any man as long as he's born in the Year of the Tiger
Fool's Love She was the usual popular high school girl, now a national celebrity. He is an introvert and romantic fool, but an ardent admirer of her. When they meet again, sparks fly. Only it takes time for her to understand he is not just a one night stand.
Kimi Wa Petto A weird story about an older career woman who takes in a younger male because he seems homeless. She treats him like her pet, washing his hair in the tub, cuddling with him at the couch and all that. Meanwhile she dates another man and doesn't think much of it.
I Do I Do This show has the usual k-drama elements: the rich glamorous boss, who doesn't think too much about the naive younger employee after a one night stand...except it is all in reverse. The female lead is the boss.