Heterogeneous bicycle traffic flows, consisting of electric bicycles (e-bicycles) and regular bicycles (r-bicycles), have become the main traffic form on shared bicycle routes in China due to the increasing number of e-bicycles. As a result, overtaking occurs frequently among bicycles, which affects cyclists’ safety and perception. This paper presents an analytical model to estimate the number of passing events in heterogeneous bicycle traffic flows. The relationships between passing events and the parameters of the heterogeneous bicycle traffic flow is established in the proposed model. The probability density functions of the speed of r-bicycles and e-bicycles are taken into consideration. The results of the model analysis show that the number of passing events increases with an increase in the flow rate and density. Both a difference in speed between different types of bicycle and the standard deviation of speed of each type of bicycle have positive correlations with the number of passing events. In addition, when the proportion of e-bicycles increases, the number of passing events first increases, and then decreases. The proposed model is calibrated against field data collected in Hangzhou. The results show that the model prediction is consistent with field observations. The model proposed in this paper provides an analytical approach to study the relationship between the characteristics of heterogeneous bicycle traffic flows and the number of passing events. This work can be considered a prerequisite for the development of the bicycle level of service criteria for heterogeneous bicycle flows.