The electronic states of a single Bi(111) bilayer and its edges, suggested as a two-dimensional topological insulator, are investigated by scanning tunneling spectroscopy (STS) and first-principles calculations. Well-ordered bilayer films and islands with zigzag edges are grown epitaxially on a cleaved crystal. The calculation shows that the band gap of the Bi bilayer closes with a formation of a new but small hybridization gap due to the strong interaction between Bi and . Nevertheless, the topological nature of the Bi bilayer and the topological edge state are preserved only with an energy shift. The edge-enhanced local density of states are identified and visualized unambiguously by STS in good agreement with the calculation. This is a clear sign of the topological edge state, which corresponds to the quantum spin Hall state. The interfacial state between Bi and is also identified inside the band gap region. This state exhibits a subtle edge modulation, which was previously interpreted as the evidence of the topological edge state [Yang , Phys. Rev. Lett. 109, 016801 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.016801].