Reproductive scientists and couples attempting pregnancy are interested in identifying predictors of the day-specific probabilities of conception in relation to the timing of a single intercourse act. Because most menstrual cycles have multiple days of intercourse, the occurrence of conception represents the aggregation across Bernoulli trials for each intercourse day. Because of this data structure and dependency among the multiple cycles from a woman, implementing analyses has proven challenging. This article proposes a Bayesian approach based on a generalization of the Barrett and Marshall model to incorporate a woman-specific frailty and day-specific covariates. The model results in a simple closed form expression for the marginal probability of conception, and has an auxiliary variables formulation that facilitates efficient posterior computation. Although motivated by fecundability studies, the approach can be used for efficient variable selection and model averaging in general applications with categorical or discrete event time data.