Robotic perception is currently at a cross-roads between modern methods which operate in an efficient latent space, and classical methods which are mathematically founded and provide interpretable, trustworthy results. In this paper, we introduce a Convolutional Bayesian Kernel Inference (ConvBKI) layer which explicitly performs Bayesian inference within a depthwise separable convolution layer to simultaneously maximize efficiency while maintaining reliability. We apply our layer to the task of 3D semantic mapping, where we learn semantic-geometric probability distributions for LiDAR sensor information in real time. We evaluate our network against state-of-the-art semantic mapping algorithms on the KITTI data set, and demonstrate improved latency with comparable semantic results.