Emerging diseases caused by coronaviruses of likely bat origin (e.g. SARS, MERS, SADS and COVID-19) have disrupted global health and economies for two decades. Evidence suggests that some bat SARS-related coronaviruses (SARSr-CoVs) could infect people directly, and that their spillover is more frequent than previously recognized. Each zoonotic spillover of a novel virus represents an opportunity for evolutionary adaptation and further spread; therefore, quantifying the extent of this "hidden" spillover may help target prevention programs. We derive biologically realistic range distributions for known bat SARSr-CoV hosts and quantify their overlap with human populations. We then use probabilistic risk assessment and data on human-bat contact, human SARSr-CoV seroprevalence, and antibody duration to estimate that ∼400,000 people (median: ∼50,000) are infected with SARSr-CoVs annually in South and Southeast Asia. These data on the geography and scale of spillover can be used to target surveillance and prevention programs for potential future bat-CoV emergence.