We present a general analytical method for obtaining unbiased prevalence estimates based on data from regional or national testing programs, where individual participation in the testing program is voluntary but where additional questionnaire data is collected regarding the individual-level reason/motivation for being tested. The approach is based on re-writing the conditional probabilities for being tested, being infected, and having symptoms, so that a series of equations can be defined that relate estimable quantities (from test data and questionnaire data) to the result of interest (an unbiased estimate of prevalence). The final estimates appear to be robust based on prima-facie examination of the temporal dynamics estimated, as well as agreement with an independent estimate of prevalence. Our approach demonstrates the potential strength of incorporating questionnaires when testing a population during an outbreak, and can be used to help obtain unbiased estimates of prevalence in similar settings.