The sudden loss of smell is among the earliest and most prevalent symptoms of COVID-19 when measured with a clinical psychophysical test. Research has shown the potential impact of frequent screening for olfactory dysfunction, but existing tests are expensive and time consuming. We developed a low-cost ($0.50/test) rapid psychophysical olfactory test (KOR) for frequent testing and a model-based COVID-19 screening framework using a Bayes Network symptoms model. We trained and validated the model on two samples: suspected COVID-19 cases in five healthcare centers (n = 926; 33% prevalence, 309 RT-PCR confirmed) and healthy miners (n = 1,365; 1.1% prevalence, 15 RT-PCR confirmed). The model predicted COVID-19 status with 76% and 96% accuracy in the healthcare and miners samples, respectively (healthcare: AUC = 0.79 [0.75–0.82], sensitivity: 59%, specificity: 87%; miners: AUC = 0.71 [0.63–0.79], sensitivity: 40%, specificity: 97%, at 0.50 infection probability threshold). Our results highlight the potential for low-cost, frequent, accessible, routine COVID-19 testing to support society's reopening.