Ocean color (OC) remote sensing requires compensation for atmospheric scattering and absorption (aerosol, Rayleigh, and trace gases), referred to as atmospheric correction (AC). AC allows inference of parameters such as spectrally resolved remote sensing reflectance (Rrs(λ);sr-1) at the ocean surface from the top-of-atmosphere reflectance. Often the uncertainty of this process is not fully explored. Bayesian inference techniques provide a simultaneous AC and uncertainty assessment via a full posterior distribution of the relevant variables, given the prior distribution of those variables and the radiative transfer (RT) likelihood function. Given uncertainties in the algorithm inputs, the Bayesian framework enables better constraints on the AC process by using the complete spectral information compared to traditional approaches that use only a subset of bands for AC. This paper investigates a Bayesian inference research method (optimal estimation [OE]) for OC AC by simultaneously retrieving atmospheric and ocean properties using all visible and near-infrared spectral bands. The OE algorithm analytically approximates the posterior distribution of parameters based on normality assumptions and provides a potentially viable operational algorithm with a reduced computational expense. We developed a neural network RT forward model look-up table-based emulator to increase algorithm efficiency further and thus speed up the likelihood computations. We then applied the OE algorithm to synthetic data and observations from the moderate resolution imaging spectroradiometer (MODIS) on NASA's Aqua spacecraft. We compared the Rrs(λ) retrieval and its uncertainty estimates from the OE method with in-situ validation data from the SeaWiFS bio-optical archive and storage system (SeaBASS) and aerosol robotic network for ocean color (AERONET-OC) datasets. The OE algorithm improved Rrs(λ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative Rrs(λ), which often appears in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level Rrs(λ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.