We present the first systematic study of the stellar populations of ultra-diffuse galaxies (UDGs) in the field, integrating the large area search and characterization of UDGs by the SMUDGes survey with the twelve-band optical photometry of the S-PLUS survey. Based on Bayesian modeling of the optical colors of UDGs, we determine the ages, metallicities, and stellar masses of 100 UDGs distributed in an area of ∼330 deg2 in the Stripe 82 region. We find that the stellar masses and metallicities of field UDGs are similar to those observed in clusters and follow the trends previously defined in studies of dwarf and giant galaxies. However, field UDGs have younger luminosity-weighted ages than do UDGs in clusters. We interpret this result to mean that field UDGs have more extended star formation histories, including some that continue to form stars at low levels to the present time. Finally, we examine stellar population scaling relations that show that UDGs are, as a population, similar to other low surface brightness galaxies.