The absence of air resistance and gravity would make a speeding bullet travel very differently in space. Although there would be no oxygen, bullets contain their own oxidiser, which would allow the gunpowder to ignite and fire the gun. With no air to slow it down, a bullet could in theory travel forever through deep space, although its path would be curved by the gravitational fields of large planets or other bodies. Floating freely in space, the recoil from the gun would also spin you in the opposite direction, a motion that would be harder to control without gravity holding you in place.
That would be interesting to observe.