Instead of the giant Yao Ming type, why not go the opposite route?
She's quite petite, even for Chinese. However she's got a bottomless pit for a stomach and can easily win any eating contest and maybe even any drinking contest. Another possibility with the petiteness is she KO'd a giant of a man attempting to touch her when she didn't want to be touched (truth be known, he was quite drunk and had a glass jaw) and maybe even likes getting into barfights or at least starting them, using the confusion to acquire some funds (unconscious people tend to be easier to pickpocket). As for habits, she pops her joints before she's about to do something strenuous like Bruce Lee did before facing Chuck Norris (Return of the Dragon?).
As for why the Triad sold her off, there's the 'she's eating us out of house and home!' route or the man she clocked happened to be someone very important (or closely related). Another possibility is even simpler: her father (or some other relative) got too much into debt (maybe using her as collatoral) and off she went. Yeah, watching Samurai Champloo. At least I didn't suggest her perfume smelled of sunflowers.
Or her 'calling card' could be the underused dart as a weapon or better yet use playing cards (using dart stats) as throwing weapons? Given that card games were popular in the Old West, tossing a playing card and lodging it into wood might stand out. Poker chips could be another potentially lethal weapon for her.