There are many dramas that are like that. "Flower of Evil" is definitely one as is "Scarlet Heart: Ryeo". Lee Joon Gi is ML in both. Most of the dramas are arrogant bad boy MLs who fall for the FL. It depends on how bad or aloof you want them to be.Try "Boys over Flowers", "Meteor Garden", "Master Devil Please Don't Kiss Me Seasons 1 and 2". Read the synopsis of any and they will tell you what you are looking for. Personally I would ei her go through the MyDramaList or go to Vikki where you can read about the story line and get to choose. One does come to mind and that is "The King's Woman" But , most start off where the ML is arrogant and bad but there is always a story as to why. I hope you search these places and I guarantee you will find what you are looking for because it depends on your personal taste and what you consider Bad and the era /genre as well. Good Luck and Happy watching.