Can refer to the six shots on a revolver, her having six guns (each with their own name, naturally*), or her nearly-supernatural abilities to follow her enemies and show up behind them (”on their six.”)
Pecos Bill might be an old man or even a myth-spirit in the way of Discworld gods (dependent on belief, fading away without it), the elderly mentor who devotes himself to training a hero/chosen one/heir to be better than he ever was. She can represent the future of the art while the old white guy represents the past, as an inversion of both many martial arts movies and many westerns where Asian and Native American characters, respectively, pass their torches to the white dude.
*The guns are named things like Golden Sunset and Deep Canyon and Silence After Battle, poetically referencing both the vibrant geography of the Old West and the weapon’s function of ending lives.