The reason why sonic flow is the most likely outcome is because in a long pipe, the friction will always push the velocity to mach 1. If we exit the air nozzle subsonically, then we will only experience one transition (subsonic>sonic), while if the flow is sonic at the nozzle, it will be accelerated to supersonic immediately after the air nozzle, and eventually settle down to sonic at some point down the barrel (sonic>supersonic>sonic). My assumption that the friction would push flow to sonic by friction probably doesn't apply to our situation because our barrels are too short. 

If we stick a bb in the flow, I believe that the flow passes by the bb, it will experience conditions similar to a converging/diverging nozzle, which means that it is very likely that the bb is within the transonic regime for a large portion of its time within the barrel. The flow immediately after passing the bb will be supersonic, so as this supersonic flow collides with the sonic flow ahead of the bb, the low pressure supersonic flow combines with the lower pressure sonic flow, creating a vortex around the front upper half of the bb. 

In this case, we can see that a high initial pressure/low barrel length might be advantageous. Compared to the 2 transitions of the previous two cases (subsonic>sonic and sonic>supersonic>sonic), we see that it is possible to keep the flow supersonic the entire length of the barrel. Initially, the flow is supersonic immediately after leaving the air nozzle, is slowed as it passes by the bb, and possibly remains supersonic the entire time, we now achieve a single flow regime throughout the entire barrel. 

Similarly, I believe that "barrel pop" is a result of a sonic flow accelerating past the bb and hitting supersonic as the bb exits the barrel.