The "omnigenic" model of the genetic architecture of complex traits proposed two categories of causal genes: core and peripheral. Core genes are hypothesized to directly regulate disease and may serve as therapeutic targets. Using a cell-type- and time-point-specific gene co-expression network for mineralizing osteoblasts, we identify a co-expression module enriched for genes implicated by bone mineral density (BMD) genome-wide association studies (GWASs), correlated with in vitro osteoblast mineralization and associated with skeletal phenotypes in human monogenic disease and mouse knockouts. Four genes from this module (B4GALNT3, CADM1, DOCK9, and GPR133) are located within the BMD GWAS loci with colocalizing expression quantitative trait loci (eQTL) and exhibit altered BMD in mouse knockouts, suggesting that they are causal genetic drivers of BMD in humans. Our network-based approach identifies a "core" module for BMD and provides a resource for expanding our understanding of the genetics of bone mass.