Angle-resolved photoemission measured from the Bi(111) surface with synchrotron radiation between 7.5 and 100 eV exhibit strong features associated with valence-band states of$p$ and$s$ symmetry and electronic surface states. The valence-band dispersions of$p$ and$s$ states have been measured along the symmetry line$\Gamma \Lambda T$ of the Brillouin zone, which is mapped out by recording normal emission at 300 K and below 20 K, and by discussing the photoemission results in terms of the direct-transition model. The experimental bulk electronic structure is compared with the results of band-structure calculations, obtained by a pseudopotential approach (Golin) and a relativistic augmented-plane-wave (Ferreira) method. Finally, two narrow nondispersing peaks observed in the low-temperature photoemission spectra at binding energies 0.40 and 2.95 eV are assigned to surface (or resonance) states.