All of the reasons you say are correct.
The bullet bumps into air molecules, speeding them up. This slows the bullet.
The air molecules are bumped forward, crowding into air already present. More molecules are now in the region than would normally be. The density goes up. Since that region has extra molecules bumping into a neighboring region, the force exerted on the neighbor is above normal. The pressure goes up.
As the bullet passes, it leaves a region where molecules have all been pushed away. Air rushes in because neighbors bump it in that direction. There are fewer molecules than normal. Density and pressure are low. Note that this means fewer molecules bump into the bullet from behind.
So there are two ways of saying this.
Lots of molecules bump into the bullet from the front, slowing it down. Few molecules bump into it from the front, which means not many bumps speed it up. This slows the bullet.
Or you can say air pressure is high in front of the bullet and low behind. These exert a greater force backward than forward. This slows the bullet.
This mechanism is dominant in almost all normal fluid flow. Friction also plays a role, but it dominates only in small, slow motion or when the fluid is extra viscous. The Reynolds number helps figure out which mechanism is dominant. It is the ratio of two kinds of forces: the force created by pushing air around and forces of friction.
A rule of thumb: in air at usual speeds, the Reynolds number is large unless the system is insect size or smaller. A bullet is heavier than a typical insect and travels much faster.