  Context. Extremely reddened AGB stars lose mass at high rates of >10^-5
Msun/yr. This is the very last stage of AGB evolution, in which stars in the
mass range 2.0--4.0 Msun (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. Aims. To determine the mass
range of the most reddened AGB stars in the Galactic bulge. Methods. 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. Results. 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--30,000 Lsun and mass-loss rates 10^-5--3x10^-4 Msun/yr. The
corresponding mass range is 1.1--6.0 Msun assuming solar metallicity.
Conclusions. 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.
