Can Dropping object's terminal velocity over the speed of sound?

Not with ANY shape or weight.

I'm sure it could be accomplished with a very dense, highly streamlined shape.

Try a lead javelin.

YES

a bullet fired from a gun

Terminal velocity of an object depends on the aerodynamic shape of the object, how dense the object is and how far it falls (which will determine wether or not it has had enough time to reach it's terminal velocity).  Those being the only limiting factors, yes it is possible to have a terminal velocity above the speed of sound.

A typical bomb dropped in world war 2 from 20,000 ft  would reach it's terminal velocity of about 800 m.p.h shortly before impact.   That's around or just above the speed of sound.   For more streamlined bombs ( like the 12,000lb bunker busting 'tallboy' that destroyed the concrete U-boat pens and the Tirpitz battleship) the terminal velocity was even higher.