Is there a minimum distance between a runway and a public road?
Yes, there is a minimum area that must be free of obstructions and closed to vehicles, but only for airports that have air carrier operations (see 14 CFR 139.309) or that receive FAA grants. AC 150/5300-13A - Airport Design has all the technical details; the actual distances are calculated from formulas, so there's no single answer. If you're really curious, you can read all the gory details in Chapter 3 and this FAA FAQ has a (very) simplified explanation:


  What is the size of the RSA [Runway Safety Area]?   
  
  The RSA is a rectangular box surrounding
  the runway and is based on the runway design code. The dimensions
  range from 120 feet to 500 feet in width and 240 feet to 1000 feet in
  length beyond the departure end of the runway. (see FAA Advisory
  Circular 150/5300-13, Airport Design) Generally, on airports that
  serve air carrier aircraft, the RSA extends 250 feet either side of
  the runway centerline and 1000 feet beyond each end of the runway.


You didn't mention which airport you're asking about, but presumably it's either privately owned and/or doesn't receive FAA grant money.