The dirty bomb, as a weapon of mass destruction, is a myth. Disperse the radioactive material far enough to affect a large number of people, and you disperse the radiation as well. The concentration of radioactive material decreases as the square of the radius of the area of dispersal.
Forget the bomb part. Think, instead, of some alternative dispersal method, such as the dust in Robert Heinlein's "Solution Unsatisfactory". In that story, radioactive material was dispersed by bombers. Consider a more selective dispersal, like spreading it in the concourses of, say, Penn Station in Manhattan.