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In this work we investigate and demonstrate benefits of a Bayesian approach to imitation learning from multiple sensor inputs, as applied to the task of opening office doors with a mobile manipulator. Augmenting policies with additional sensor inputs, such as RGB + depth cameras, is a straightforward approach to improving robot perception capabilities, especially for tasks that may favor different sensors in different situations. As we scale multi-sensor robotic learning to unstructured real-world settings (e.g. offices, homes) and more complex robot behaviors, we also increase reliance on simulators for cost, efficiency, and safety. Consequently, the sim-to-real gap across multiple sensor modalities also increases, making simulated validation more difficult. We show that using the Variational Information Bottleneck (Alemi et al., 2016) to regularize convolutional neural networks improves generalization to held-out domains and reduces the sim-to-real gap in a sensor-agnostic manner. As a side effect, the learned embeddings also provide useful estimates of model uncertainty for each sensor. We demonstrate that our method is able to help close the sim-to-real gap and successfully fuse RGB and depth modalities based on understanding of the situational uncertainty of each sensor. In a real-world office environment, we achieve 96% task success, improving upon the baseline by +16%.