Mass spectrometry imaging is emerging as a valuable tool for measuring in situ cancer biomarkers. In fact, it allows us to detect critical biological traits that would be overlooked with a simple visual morphological assessment of a sample. This technique measures the abundance of several specific molecules over multiple locations in a biological sample. For example, when analyzing a brain slide, it produces several profiles of molecule abundances, one for each analyzed pixel. The analysis of these complex data structures calls for developing tailored statistical methods. In this contribution, we propose employing models for nested, separately exchangeable data to estimate a biclustering solution, i.e., cluster locations characterized by similar abundance profiles, and simultaneously detect molecules with similar expressions within clusters of pixels. We analyze the brain image of a healthy mouse, comprising the mass spectra of approximately one hundred lipid molecules in approximately 1600 pixels. To address the large dimensionality of the dataset and the need for timely results, we apply a scalable coordinate ascent variational inference algorithm that dramatically scales the applicability of the model. We showcase how the estimated biclustering structure allows us to detect meaningful image segmentations and patterns of activated molecules.