How are the flat/aero bullhorn handelbars called?
These are one component of aero bars, used on  time trail and triathlon bars.

These are used in conjunction with elbow pads and bar extensions that mount on top. The attachment points are visible in the pic you provided. 

See this article Selecting the Right Aerobars for Triathlon.

Typically brake levers are mounted on the ends of the lower bars, and gear shifters on the ends of the bar extensions.

Aerodynamic bicycle components tent to be expensive because they are predominately used by pros and racers so they also need to be string and light.