The lady of exquisite debauchery
While she is a shrewd businesswoman, she has never believed in taking advantage of those who were unable to suffer it. She was, in fact, a working girl herself, and proved to the madame, Miss Rosie, that she had more on her shoulders than a pretty face through advice in the expansion of the brothel to include a small gambling den. She also encouraged the high-class feel of the establishment, though the madame was loathe to change so drastically, and only made small changes towards raising the bar.
Sophie Satin was actually quite lucky that a judge was in town and had made their acquaintence the same day that an Indian attack occured. Miss Rosie was mortally wounded in the attack, and the judge himself had heard her exclaim (perhaps in jest) that she'd be turning her business over to Sophie any day. As the witness and pleased client, he was only too happy to make the Desert Rose hers legally.
As a madame, she refuses to take any more clients, as in truth, she's never liked the rutting of commen men, but she treats her ladies well, especially when medicine and cleanliness are concerned. She also maintains a decent spectrum of ladies, so that all may afford a night or an hour within her walls, and within the arms of a lovely (or not so lovely) lady of the night. As a lady, she can drink with the best of them, and holds a certain fondness for poker, as she feels men bely their feelings in a variety if ways, if one is trained to look for the signs.
The only thing not mentioned above is a stilleto dagger in her boot and a 4-shot derringer pistol strapped to her thigh, both of which she's had to use once or twice.
Examples of what she might wear: