Disregarding the ISS’ orbital velocity, and also disregarding any gravitational influences, we can calculate time of flight for a bullet traveling the distance from Earth to Mars.
Assume 1220 m/s muzzle velocity per the OP.
Closest approach between the two: 56M km
time of flight: 531.27 days (about a year and a half)
Maximum distance betwen the two (when on opposite sides of the sun): 378,800,000 km
time of flight: 3593.7 days (almost ten years)
Firing in space, the muzzle velocity would be very slightly higher because the bullet does not have to accelerate the air in front of it inside the gun barrel. However, the mass of this air is very small (50-100 milligrams) and so its effect on the acceleration of a four-gram bullet is miniscule to begin with. Instead of 1220 m/s, you might see 1230 or 1240 m/s.
By ejecting the mass of the bullet in one direction, the ISS will be nudged in the opposite direction, but the effect will be miniscule. The bullet weighs a few grams, and the ISS weighs 376,000 kg (376,000,000 grams). If a four-gram bullet is launched from the ISS at 1220 m/s, the ISS will start moving in the opposite direction at 13 microns per second (0.0000467 km/hr) . This is additive (in vector fashion) to its orbital velocity of ~27,850 km/hr.