Measuring the prevalence of active SARS-CoV-2 infections in the general population is difficult because tests are conducted on a small and nonrandom segment of the population. However, hospitalized patients are tested at very high rates, even those admitted for non-COVID reasons. We show how to use information on testing of non-COVID hospitalized patients to obtain tight bounds on population prevalence, under conditions weaker than those usually used. We apply our approach to the population of test and hospitalization data for Indiana, and we validate our approach. Our bounds could be constructed at relatively low cost, and for other heavily tested populations.