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Confocal microscopy is essential for histopathologic cell visualization and quantification. Despite its significant role in biology, fluorescence confocal microscopy suffers from the presence of inherent noise during image acquisition. Non-local patch-wise Bayesian mean filtering (NLB) was until recently the state-of-the-art denoising approach. However, classic denoising methods have been outperformed by neural networks in recent years. In this work, we propose to exploit the strengths of NLB in the framework of Bayesian deep learning. We do so by designing a convolutional neural network and training it to learn parameters of a Gaussian model approximating the prior on noise-free patches given their nearest, similar yet non-local, neighbors. We then apply Bayesian reasoning to leverage the prior and information from the noisy patch in the process of approximating the noise-free patch. Specifically, we use the closed-form analytic \textit{maximum a posteriori} (MAP) estimate in the NLB algorithm to obtain the noise-free patch that maximizes the posterior distribution. The performance of our proposed method is evaluated on confocal microscopy images with real noise Poisson-Gaussian noise. Our experiments reveal the superiority of our approach against state-of-the-art unsupervised denoising techniques.