Blood and tissue are composed of many functionally distinct cell subsets. In immunological studies, these can be measured accurately only using single-cell assays. The characterization of these small cell subsets is crucial to decipher system-level biological changes. For this reason, an increasing number of studies rely on assays that provide single-cell measurements of multiple genes and proteins from bulk cell samples. A common problem in the analysis of such data is to identify biomarkers (or combinations of biomarkers) that are differentially expressed between two biological conditions (e.g. before/after stimulation), where expression is defined as the proportion of cells expressing that biomarker (or biomarker combination) in the cell subset(s) of interest. Here, we present a Bayesian hierarchical framework based on a beta-binomial mixture model for testing for differential biomarker expression using single-cell assays. Our model allows the inference to be subject specific, as is typically required when assessing vaccine responses, while borrowing strength across subjects through common prior distributions. We propose two approaches for parameter estimation: an empirical-Bayes approach using an Expectation-Maximization algorithm and a fully Bayesian one based on a Markov chain Monte Carlo algorithm. We compare our method against classical approaches for single-cell assays including Fisher's exact test, a likelihood ratio test, and basic log-fold changes. Using several experimental assays measuring proteins or genes at single-cell level and simulations, we show that our method has higher sensitivity and specificity than alternative methods. Additional simulations show that our framework is also robust to model misspecification. Finally, we demonstrate how our approach can be extended to testing multivariate differential expression across multiple biomarker combinations using a Dirichlet-multinomial model and illustrate this approach using single-cell gene expression data and simulations.