Same goes for exceeding the speed of sound. Some areas on the bullet will begin to experience subsonic flow (and so enter the transonic region) before the bullet slows to the speed of sound.
The first time a concerted effort was made to study compressibility effect was with Kelly Johnson's P-38 Lightning. It was experiencing control problems in power-on dives at about 0.67 Mach. Even when the aircraft itself was yet far below the speed of sound, airflow over small regions of it were reaching the speed of sound, which created shock waves that were monkeying with the control surfaces.
Basically it was bumping into the bottom of the transonic region (a speed known as the lower critical mach number) and it wasn't designed to deal with the complications that caused.
Here's an image from the P-38's operator's manual admonishing the pilots not to exceed 0.67 Mach:
The evil compressibility was waiting for you if you dared exceed Mach 0.67.
Chuck Yeager and the builders of the Bell X-1 knew to expect problems when they had reached the lower critical Mach number but there were no wind tunnels that could reproduce the speeds of the X-1, so Yeager was making it up as he went.
It's not the speed of sound that's the problem, it's the transonic region that surrounds it that's the bugbear. A bullet never goes from supersonic directly to subsonic, it always slows from supersonic first to transonic and then to subsonic, literally never having any idea when it crossed the "speed of sound."
You'll have seen evidence of that if you've ever looked at the drag curve diagram for a bullet.
(diagram sourced from Bryan's Litz's "Applied Ballistics for Long Range Shooting")
Going from left to right, the drag begins to climb steeply well before reaching the speed of sound, which is an indication that the bullet is above the critical mach number and so is experiencing a new type of drag, the wave form drag that always accompanies a shock wave.
Which also brings up another reason why match .22LR ammunition is usually subsonic. Most .22LR projectiles have round or elliptical noses, not the spire-point design that would benefit supersonic flight. If you drove them to slightly supersonic speeds, because of their aerodynamic inefficiency, they wouldn't remain supersonic very long anyway. Drag tends to be so much lower at subsonic velocities that it's more economical to give up that 150 fps or so and start out subsonic.
So it turns out the world isn't as simple as black and white, supersonic or subsonic. There's a lot of degrees of gray in between.