Some of that old-fashioned sexism from the MC I see, and for a guy that thought about what a 'peaceful' person he was what with growing up in China and all he certainly has zero problems executing dozens of people without the slightest hesitation or remorse.
I assume bullets travel with a variety of velocities depending on whatever but most bullets aren't sub sonic so we know that unless twice the speed of an average man is supersonic (no) he won't be able to dodge bullets.
He should be able to dodge a bullet now if there's conditions are met; The distance is a good enough distance away (few meters), he knows where it's coming from, and he's competent enough to react.