This study serves as a proof of concept for a Bayesian variational framework enabling high-resolution 3D activity reconstruction in 220 liter waste drums using Angular Segmented Gamma Scanning (ASGS) data and transmission-derived attenuation maps. Our proposed inference and uncertainty quantification approach is demonstrated using virtual experiments that simulate typical waste characterization scenarios. Computations are made tractable by using stochastic variational inference (SVI) together with a multi-resolution spatial prior to infer the spatial activity distribution. Results show that the approach can recover the spatial activity distribution within the considered drum, while also providing more accurate total activity estimates than conventional methods, thereby enhancing the accuracy of radiological waste characterization.