The Bi͑111͒ surface was studied by scanning tunneling microscopy ͑STM͒, transmission electron microscopy ͑TEM͒, and angle-resolved photoemission spectroscopy ͑ARPES͒ in order to verify the existence of a recently proposed surface charge-density wave ͑CDW͒ ͓Ch. R. Ast and H. Höchst, Phys. Rev. Lett. 90, 016403 ͑2003͔͒. The STM and TEM results do not support a CDW scenario at low temperatures. Furthermore, the quasiparticle interference pattern observed in STM confirms the spin-orbit split character of the surface states which prevents the formation of a CDW, even in the case of good nesting. The dispersion of the electronic states observed with ARPES agrees well with earlier findings. In particular, the Fermi contour of the electron pocket at the center of the surface Brillouin zone is found to have a hexagonal shape. However, no gap opening or other signatures of a CDW phase transition can be found in the temperature-dependent data.