Virginia Railway Express has the Dinky beat. Crystal City in Arlington, Virginia, to L'Enfant Plaza in Washington, DC, approximately 2 miles: one way, $6.75.
It's ironic that VRE's fares between Washington (zone 1) and Arlington and Alexandria (zone 2) keep going up, because it's one of the few places where VRE has empty seats to sell. A lot of commuters get off at Crystal City going north and board there going south. I myself have a zone 2 monthly ticket from Fredericksburg; if I have to go into Washington, I get off VRE and ride the Metro rather than buy a $6.75 one-way ticket to go at most 4 miles (if I go all the way to Union Station).