New generation geostationary satellites make solar reflectance observations available at a continental scale with unprecedented spatiotemporal resolution and spectral range. Generating quality land monitoring products requires correction of the effects of atmospheric scattering and absorption, which vary in time and space according to geometry and atmospheric composition. Many atmospheric radiative transfer models, including that of Multi-Angle Implementation of Atmospheric Correction (MAIAC), are too computationally complex to be run in real time, and rely on precomputed look-up tables. Additionally, uncertainty in measurements and models for remote sensing receives insufficient attention, in part due to the difficulty of obtaining sufficient ground measurements. In this paper, we present an adaptation of Bayesian Deep Learning (BDL) to emulation of the MAIAC atmospheric correction algorithm. Emulation approaches learn a statistical model as an efficient approximation of a physical model, while machine learning methods have demonstrated performance in extracting spatial features and learning complex, nonlinear mappings. We demonstrate stable surface reflectance retrieval by emulation (R2 between MAIAC and emulator SR are 0.63, 0.75, 0.86, 0.84, 0.95, and 0.91 for Blue, Green, Red, NIR, SWIR1, and SWIR2 bands, respectively), accurate cloud detection (86\%), and well-calibrated, geolocated uncertainty estimates. Our results support BDL-based emulation as an accurate and efficient (up to 6x speedup) method for approximation atmospheric correction, where built-in uncertainty estimates stand to open new opportunities for model assessment and support informed use of SR-derived quantities in multiple domains.