Bi-induced (square-root 3 X square-root 3)R30-degrees structures formed on the Si(111) surface are studied using scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED). Three distinct phases are identified depending on the Bi coverage : monomer, trimer, and honeycomb phases. The square-root 3 X square-root 3 symmetry is preserved for these phases in the LEED observation. At low coverages, Bi atoms are found to occupy the T4 site. In this adsorption geometry, the monomer phase (alpha phase) is formed stably up to the ideal coverage of 1/3 ML (ML=monolayer). In the trimer phase (beta phase) at the saturation coverage of 1 NIL, the individual atoms of the Bi clusters are clearly resolved. Between these two coverages, however, a honeycomb-type square-root 3 X square-root 3 reconstruction has also been found by the STM to coexist with the trimer phase. This result reveals a new coverage dependent reconstruction process involving the square-root 3 X square-root 3 reconstruction of the Si(111) surface.