nah its all about aerodynamics, back in the early days when aircraft were just beginning to push into the realms of supersonic flight, they found all sorts of problems crossing the sound barrier, particlarly with regard to the complete loss of pitch control- the control surfaces (elevators) no longer had any effect on the attitude of the aircraft during this transonic speed and above.
The problem was in the design of the control surfaces. Previously, the control surfaces (the part that moves) were on the trailing edge of the tailplane and worked fine up to the speed of sound. They found that when flying at supersonic speeds, these control surfaces became buffeted in the shockwave of the aircraft fuselage, wings, and tail etc and were stalled in this turbulent airflow to the aft of the aircraft so therefore no longer were effective. To solve the issue, they changed the design of the tail, and all supersonic aircraft share this design today.... The entire horizontal stabiliser now moves instead of just a strip at trailing edge. Problem solved.
So i believe the stability of a transonic bullet has to do with aerodynamics and therefore the shape of the bullet.