As long as gravity is orthogonal to the surface, I don't think it makes any difference whether the surface is flat or convex - gravity will pull the bullet toward the surface. To fit the physics, a flat earth would need "lines of gravity" that were parallel instead of convergent at the center of mass. The theory would be different but the observations would be the same.
The curvature definitely makes a difference - otherwise satellites wouldn't stay in orbit.
Consider the following childish drawing. The blue lines are the velocity vector at time A, the yellows at time B. The red lines are supposed to represent acceleration towards the centre of the earth due to gravity,
In the round earth case, the satellite is being accelerated towards the centre of the earth, but due to it's momentum orthogonal to the earth doesn't approach the surface, since the surface is curving away. Putting an object in stable orbit is all about calculating the right forward (orthogonal to the radius of the earth) speed (square root of the acceleration due to gravity multiplied by the distance to the centre of the earth).
In the flat earth case, in contract, acceleration due to gravity would eventually bring the satellite crashing to the ground regardless of it's speed (unless it overshot the edge).
By my count, a bullet would need to be travelling at only a little over 7.9 km/s a second to achieve orbital velocity and never hit the ground - at least if there was neither air resistance nor pesky things like trees, buildings and hills to get in the way.