Differential network analysis plays an important role in learning how gene interactions change under different biological conditions, and the high resolution of single-cell RNA (scRNA-seq) sequencing provides new opportunities to explore these changing gene-gene interactions. Here, we present a sparse hierarchical Bayesian factor model to identify differences across network structures from different biological conditions in scRNA-seq data. Our methodology utilizes latent factors to impact gene expression values for each cell to help account for zero-inflation, increased cell-to-cell variability, and overdispersion that are unique characteristics of scRNA-seq data. Condition-dependent parameters determine which latent factors are activated in a gene, which allows for not only the calculation of gene-gene co-expression within each group but also the calculation of the co-expression differences between groups. We highlight our methodology's performance in detecting differential gene-gene associations across groups by analyzing simulated datasets and a SARS-CoV-2 case study dataset.