Basic physics: the bullet will start to fall as soon as it leaves the muzzle. Since it does not have an airfoil, there's nothing to make it rise, except the inclination of the barrel.
There's a classic physics riddle concerning this: in an ideal world (vacuum, no curvature of the earth), if you fire a gun and drop a bullet on the ground at the exact moment the fired bullet leaves the muzzle, which will hit the ground first? Answer: they both hit the ground at the same time.
Bullets appear to rise because the barrel is inclined upward to hit a distant target. Think of the trajectory of