Growth of ultra-thin Au films on Si(1 1 1)root 3 x root 3-Bi surfaces was studied using low energy electron diffraction, scanning tunneling microscopy and in situ measurements of surface conductivity. The Si(1 1 1)root 3 x root 3-Bi surfaces were represented either by the Si(1 1 1)-alpha-root 3 x root 3-Bi phase with 0.33 ML (monolayers) of Bi adatoms or by the Si(1 1 1)-beta-root 3 x root 3-Bi phase with 1.0 ML of Bi atoms arranged into trimers. Structure of the template surface was found to affect greatly the growth mode and conductance of the overgrown Au films in the thickness range from 0.1 to 3.0 ML of Au. Growth of Au films on Si(1 1 1)-beta-root 3 x root 3-Bi follows the Vollmer-Webber mode, while in case of Au films on Si(1 1 1)-alpha-root 3 x root 3-Bi the complicated multi-stage growth occurs where formation of Stranski-Krastanov wetting layer is successively followed by island growth and vice versa. Surface conductivity of the samples was found to be dictated by Au film morphology. In the Au/Si(1 1 1)-beta-root 3 x root 3-Bi sample, surface conductivity remains essentially unchanged due to lacking of electrical connections between Au islands. In the Au/Si(1 1 1)-alpha-root 3 x root 3-Bi sample, surface conductivity grows with Au thickness starting from overcoming of percolation threshold at similar to 0.6 ML of Au.