Traditional accident risk prediction models need adequate data on explanatory variables, most importantly data on traffic flows. However, in the case of accidents between bicycles the availability of such data is often limited. Therefore, alternative bottom-up simulation modelling approaches are expected to complement traditional equation-based models. In this paper we present an agent-based approach to explore bicycle-bicycle accidents. Specifically, we hypothesise that (1) bicycle-bicycle accidents are based on the population of encounters between cyclists rather than on bicycle flows and (2) that encounters have a non-linear relationship with flows. Bicycle flows and encounters are simulated by means of an agent-based model that is implemented for the road network of the city of Salzburg. Simulation results are tested against a 10-year dataset of police records on bicycle-bicycle accidents. The results affirm both hypotheses: First, cyclist encounters exhibit a linear relationship to accidents and thus suggest being the true population of bicycle-bicycle accidents. Second, flows show a relationship in the form of a second-order polynomial function with encounters as well as accidents.