Single-crystalline films of Lu3Al5O12:Bi, prepared by the liquid phase epitaxy method from the melt-solution based on Bi2O3 flux, have been studied at 4.2-400 K by time-resolved luminescence spectroscopy methods. Their emission spectra consist of two types of bands with strongly different characteristics. The ultraviolet emission band consists of two components, arising from the electronic transitions which correspond to the and transitions in a free Bi3+ ion. At low temperatures, mainly the lower-energy component of this emission is observed, having the decay time~10-3 s at T < 100 K and arising from the metastable 3P0 level. At T > 100 K, the higher-energy emission component appears, arising from the thermally populated emitting 3P1 level. The visible emission spectrum consists of two dominant strongly overlapped broad bands with large Stokes shifts. At 4.2 K, their decay times are ~10-5 s and decrease with increasing temperature. Both of the visible emission bands are assumed to have an exciton origin. The lower-energy band is ascribed to an exciton, localized near a single Bi3+ ion. The higher-energy band shows a stronger intensity dependence on the Bi3+ content and is assumed to arise from an exciton localized near a dimer Bi3+ center. The origin and structure of the corresponding excited states is considered and the processes, taking place in the excited states, are discussed.