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 \ga 0.34 ) PNe are estimated to be between 0.58 and 0.62 { M } _ { \sun } .
The oxygen abundance in form \log { ( 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 { M } _ { \sun } with Y _ { ZAMS } \approx 0.31 - 0.33 and Z _ { ZAMS } \approx 0.19 - 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 \sim 4 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 \approx 0.32 ) on the main sequence and their ages are between 2 and 4 Gyrs .

The chemical evolution of nitrogen in the Galactic bulge inferred from the models is consistent with the cosmic evolution inferred from HII regions and unevolved stars .
The inferred ZAMS N/O ratio ( \log { N / O } \approx - 0.35 ) of bulge PNe with the largest CSPN masses are shown to be above the solar ratio .
The inferred ZAMS N/O ratios of the entire range of PNe metallicities is consistent with both primary and secondary production of nitrogen contributing to the chemical evolution of nitrogen in the Galactic bulge .

The inferred ZAMS value of C/O is less than 1 .
This indicates the mass of the PNe progenitors are low enough ( M \la 1.8 { M } _ { \sun } ) to not produce carbon stars via the third dredge-up .