First-principle study of possible bismuth-related centers in SiO2 and GeO2 glass model hosts is performed and the results are compared with the experimental data. The following centers are modeled: trivalent and divalent Bi substitutional centers; BiO interstitial molecule; interstitial ion, Bi+, and atom, Bi0; Bi··· ≡Si–Si≡ and Bi··· ≡Ge–Ge≡ complexes formed by interstitial Bi atoms and glass intrinsic defects, ≡Si–Si≡ or ≡Ge–Ge≡ oxygen vacancies; interstitial dimers, Bi20 and Bi2−. Experimental data available on bismuth-related IR luminescence in SiO2:Bi and GeO2:Bi glasses, visible (red) luminescence in SiO2:Bi glass and luminescence excitation are analyzed. A comparison of calculated spectral properties of bismuth-related centers with the experimental data shows that the IR luminescence in SiO2:Bi and GeO2:Bi is most likely caused by Bi··· ≡Si–Si≡ and Bi··· ≡Ge–Ge≡ complexes, and divalent Bi substitutional center is responsible for the red luminescence in SiO2:Bi.