implies that you are running so hard that your buttocks fall off. Obviously that never happens, but it is a figurative way of stating that you are doing something to the point of exhaustion and beyond. It is a familiar trope used with other pursuits as well:
I worked my ass off on that project.
We're going to party our asses off once we graduate.
It is a popular idiom though it has a wide range of meaning depending on the context. In your example I would venture to say, though not having read the book, that it's a compliment implying the woman is brazen or brave. "She has style" is a complementary idiom that usually means the woman did something "in her own unique way" or "in an unexpected way."
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It's a quaint/inventive conflation of...