Why is a reciprocating engine air intake a reverse bell shape?
It's simply a NACA duct inlet.  On a fully parallel to flow flush surface it has some (but not all) of the effectiveness of a protruding scoop, without the drag.  The curved sides of the ramp act like vortex generators, with the rotation of the vortices on each side pulling air down into the ramp.
On a very clean airplane like one of the RV series homebuilts, that kind of duct can have a measurable benefit.  On a plane like the one pictured, there is a theoretical benefit drag wise, but it would make little detectable difference in that sort of a light plane (with its unfaired nose gear) and is mostly for looks.
In fact since the surface isn't really parallel to the airflow but curves in, the opening is presented more or less directly into the airstream for ram effect and there really isn't a need to create vortices to pull air down the ramp.  A straight sided ramp would work just as well in that particular instance.  Looks cool though, which I suspect is the main reason it's being used there.