Recent literature has reported a high percentage of asymptomatic or paucisymptomatic cases in subjects with COVID-19 infection. This proportion can be difficult to quantify; therefore, it constitutes a hidden population. This study aims to develop a proof-of-concept method for estimating the number of undocumented infections of COVID-19. This is the protocol for the INCIDENT (Hidden COVID-19 Cases Network Estimation) study, an online, cross-sectional survey with snowball sampling based on the network scale-up method (NSUM). The original personal network size estimation method was based on a fixed-effects maximum likelihood estimator. We propose an extension of previous Bayesian estimation methods to estimate the unknown network size using the Markov chain Monte Carlo algorithm. On 6 May 2020, 1963 questionnaires were collected, 1703 were completed except for the random questions, and 1652 were completed in all three sections. The algorithm was initialized at the first iteration and applied to the whole dataset. Knowing the number of asymptomatic COVID-19 cases is extremely important for reducing the spread of the virus. Our approach reduces the number of questions posed. This allows us to speed up the completion of the questionnaire with a subsequent reduction in the nonresponse rate.