The frequency dependent dielectric constant and loss of the unconventional bismuth cuprate glasses have been presented in wide temperature and frequency ranges. Alternating current dielectric loss peak has been observed in the measurable frequency range at higher temperatures, where the measured ac conductivity approaches the dc conductivity. The temperature range where ac loss peak has been observed, varies systematically with glass composition. The dielectric data at these temperature ranges have been analyzed in terms of different theoretical models to find out the possible relaxation mechanism. It has been observed that the dipolar relaxation model with a distribution of relaxation times can best explain the experimental data. The dipolar relaxation occurs due to the hopping of charge carriers between different localized valence states of copper ions within a range of energies near the mobility edge. High value of the dielectric constant observed in these glasses can be attributed to the influence of high polarizability of the Bi3+ ions of the unconventional network former Bi2O3 to the ac response. The higher distribution of the relaxation times in the present glasses compared to the unconventional lead cuprate glasses indicates less homogeneity of the bismuth cuprate glass system.