:::No, the bound charge density really truly comes from real charges tied to the vicinity of a site. The problem is that you want to smear out the dipole moment but without introducing any charge anywhere. This is impossible. It is mathematically necassary that a smeared-out dipole moment brings positive charge to some areas and negative charge to other areas. Let's do the 1D case: A point dipole has charge distribution ρ(x) = P δ'(x). We smear it out to a dipole distribution P(y), for example P(y)=P0 e-y^2. Then the overall charge distribution is 
 ::: 
 :::(integration by parts), i.e., a finite charge which is positive in some places and negative in other places. -)