Whole-slide image (WSI) classification is fundamental to computational pathology, which is challenging in extra-high resolution, expensive manual annotation, data heterogeneity, etc. Multiple instance learning (MIL) provides a promising way towards WSI classification, which nevertheless suffers from the memory bottleneck issue inherently, due to the gigapixel high resolution. To avoid this issue, the overwhelming majority of existing approaches have to decouple the feature encoder and the MIL aggregator in MIL networks, which may largely degrade the performance. Towards this end, this paper presents a Bayesian Collaborative Learning (BCL) framework to address the memory bottleneck issue with WSI classification. Our basic idea is to introduce an auxiliary patch classifier to interact with the target MIL classifier to be learned, so that the feature encoder and the MIL aggregator in the MIL classifier can be learned collaboratively while preventing the memory bottleneck issue. Such a collaborative learning procedure is formulated under a unified Bayesian probabilistic framework and a principled Expectation-Maximization algorithm is developed to infer the optimal model parameters iteratively. As an implementation of the E-step, an effective quality-aware pseudo labeling strategy is also suggested. The proposed BCL is extensively evaluated on three publicly available WSI datasets, i.e., CAMELYON16, TCGA-NSCLC and TCGA-RCC, achieving an AUC of 95.6%, 96.0% and 97.5% respectively, which consistently outperforms all the methods compared. Comprehensive analysis and discussion will also be presented for in-depth understanding of the method. To promote future work, our source code is released at: https://github.com/Zero-We/BCL.