We apply a self-consistent and robust Bayesian statistical approach to determine the ages, distances, and zero-age main sequence (ZAMS) masses of 28 field DA white dwarfs (WDs) with ages of approximately 4-8 Gyr. Our technique requires only quality optical and near-infrared photometry to derive ages with <15% uncertainties, generally with little sensitivity to our choice of modern initial-final mass relation. We find that age, distance, and ZAMS mass are correlated in a manner that is too complex to be captured by traditional error propagation techniques. We further find that the posterior distributions of age are often asymmetric, indicating that the standard approach to deriving WD ages can yield misleading results.