Gravity doesn’t have a speed. It creates an acceleration due to force. The bullet is accelerating over a great distance until it reaches terminal velocity (where the air resistance counterbalances any gains in acceleration).

The easiest way to think about it is in terms of conservation of energy. All the kinetic energy the bullet has at the muzzle is converted into gravitational potential until velocity hits zero. At that point, gravitational velocity starts getting converted directly back into kinetic energy. If not for air resistance, the bullet would reach the ground at roughly muzzle velocity. However, air resistance on the way up zaps some of that energy and presents a velocity barrier on the way down.

There are two components - horizontal and vertical. For a bullet fired straight up, horizontal component is negligible, as the bullet will spend enough time in flight for it to decrease due to air resistance.

The vertical component is primarily determined by sectional density. Tumbling bullet spends a lot of time flying sideways, so its terminal velocity (where air resistance equals weight) is way less than muzzle velocity.

By "speed of gravity" I assume you mean terminal velocity[1].

If not fired fairly straight up the bullet can maintain a ballistic trajectory[2], rather than being in a vertical free fall. In that case, the higher speed compared to the terminal velocity is simply because it has yet to shed the speed it acquired[3] when it was accelerated out of the barrel.

[1]: https://en.wikipedia.org/wiki/Terminal_velocity

[2]: https://en.wikipedia.org/wiki/Ballistics

[3]: https://en.wikipedia.org/wiki/Muzzle_velocity

It's not. The magnitude of the velocity of a falling bullet (in the low m/s) is many orders of magnitude lower than the speed of gravity (which propagates at the speed of light)

Gravity isn’t a speed, it’s a force.