Selecting centrally quiescent galaxies from the Sloan Digital Sky Survey (SDSS) to create high signal-to-noise ratio (≳100 Å−1) stacked spectra with minimal emission-line contamination, we accurately and precisely model the central stellar populations of barred and unbarred quiescent disk galaxies. By splitting our sample by redshift, we can use the fixed size of the SDSS fiber to model the stellar populations at different radii within galaxies. At , the SDSS fiber radius corresponds to ≈1 kpc, which is the typical half-light radii of both classical bulges and disky pseudobulges. Assuming that the SDSS fiber primarily covers the bulges at these redshifts, our analysis shows that there are no significant differences in the stellar populations, i.e., stellar age, [Fe/H], [Mg/Fe], and [N/Fe], of the bulges of barred versus unbarred quiescent disk galaxies. Modeling the stellar populations at different redshift intervals from z = 0.020 to z = 0.085 at fixed stellar masses produces an estimate of the stellar population gradients out to about half the typical effective radius of our sample, assuming null evolution over this ≈1 Gyr epoch. We find that there are no noticeable differences in the slopes of the azimuthally averaged gradients of barred versus unbarred quiescent disk galaxies. These results suggest that bars are not a strong influence on the chemical evolution of quiescent disk galaxies.