Extremely reddened asymptotic giant branch stars (AGB) lose mass at high rates of >10–5M☉/yr. This is the very last stage of AGB evolution, in which stars in the mass range ∼2.0-4.0M☉ (for solar metallicity) should have been converted to C stars already. The extremely reddened AGB stars in the Galactic bulge are however predominantly O-rich, implying that they might be either low-mass stars or stars at the upper end of the AGB mass range. Our goal is to determine the mass range of the most reddened AGB stars in the Galactic bulge. Using Virtual Observatory tools, we constructed spectral energy distributions of a sample of 37 evolved stars in the Galactic bulge with extremely red IRAS colours. We fitted DUSTY models to the observational data to infer the bolometric fluxes. Applying individual corrections for interstellar extinction and adopting a common distance, we determined luminosities and mass-loss rates, and inferred the progenitor mass range from comparisons with AGB evolutionary models. The observed spectral energy distributions are consistent with a classification as reddened AGB stars, except for two stars, which are proto-planetary nebula candidates. For the AGB stars, we found luminosities in the range ∼3000-30000L☉ and mass-loss rates ∼10–5-3x10–4M☉/yr. The corresponding mass range is ∼1.1-6.0M☉ assuming solar metallicity. Contrary to the predictions of the evolutionary models, the luminosity distribution is continuous, with many O-rich AGB stars in the mass range in which they should have been converted into C stars already. We suspect that bulge AGB stars have higher than solar metallicity and therefore may avoid the conversion to C-rich. The presence of low-mass stars in the sample shows that their termination of the AGB evolution also occurs during a final phase of very high mass-loss rate, leading to optically thick circumstellar shells.