  The separation of oxygen- and carbon-rich AGB sources is crucial for their
accurate use as local and cosmological distance and age/metallicity indicators.
We investigate the use of unsupervised learning algorithms for classifying the
chemistry of long-period variables from Gaia DR3's BP/RP spectra. Even in the
presence of significant interstellar dust, the spectra separate into two groups
attributable to O-rich and C-rich sources. Given these classifications, we
utilise a supervised approach to separate O-rich and C-rich sources without
BP/RP spectra but instead given broadband optical and infrared photometry
finding a purity of our C-rich classifications of around $95$ per cent. We test
and validate the classifications against other advocated colour-colour
separations based on photometry. Furthermore, we demonstrate the potential of
BP/RP spectra for finding S-type stars or those possibly symbiotic sources with
strong emission lines. Although our classification suggests the Galactic
bar-bulge is host to very few C-rich long-period variable stars, we do find a
small fraction of C-rich stars with periods $>250\,\mathrm{day}$ that are
spatially and kinematically consistent with bar-bulge membership. We argue the
combination of the observed number, the spatial alignment, the kinematics and
the period distribution disfavour young metal-poor star formation scenarios
either in situ or in an accreted host, and instead, these stars are highly
likely to be the result of binary evolution and the evolved versions of blue
straggler stars already observed in the bar-bulge.
