  Thermally pulsing asymptotic giant branch (TP-AGB) models of bulge stars are
calculated using a synthetic model. The goal is to infer typical progenitor
masses and compositions by reproducing the typical chemical composition and
central star masses of planetary nebulae (PNe) in the Galactic bulge. The AGB
tip luminosity and the observation that the observed lack of bright carbon
stars in the bulge are matched by the models.
  Five sets of galactic bulge PNe were analyzed to find typical abundances and
central star of planetary nebulae (CSPN) masses. These global parameters were
matched by the AGB models. These sets are shown to be consistent with the most
massive CSPN having the largest abundances of helium and heavy elements. The
CSPN masses of the most helium rich (He/H$\ga$0.130 or $Y\ga0.34$) PNe are
estimated to be between 0.58 and 0.62$ {\rm M}_{\sun}$. The oxygen abundance in
form $\log{\rm (O/H)}+12$ of these highest mass CSPN is estimated to be
$\approx$8.85.
  TP-AGB models with ZAMS masses between 1.2 and 1.8$ {\rm M}_{\sun}$ with
$Y_{\rm ZAMS}\approx0.31-0.33$ and $Z_{\rm ZAMS}\approx0.19-0.22$ fit the
typical global parameters, mass, and abundances of the highest mass CSPN. The
inferred ZAMS helium abundance of the most metal enriched stars implies
$dY/dZ\sim4$ for the Galactic bulge. These models produce no bright carbon
stars in agreement with observations of the bulge. These models produce an AGB
tip luminosity for the bulge in agreement with the observations. These models
suggest the youngest main sequence stars in the Galactic bulge have enhanced
helium abundance ($Y\approx0.32$) on the main sequence and their ages are
between 2 and 4 Gyrs.
