As the number of bicyclists in urban areas continues to increase, the need to realistically model the movement and interactions of bicyclists in mixed urban traffic is rapidly gaining importance. Therefore, this paper presents an agent space model (ASM) to elucidate the movements of bicyclists and pedestrians on shared roads. The ASM model, via simulation, particularly illustrates the dispersion phenomenon observed for non-motorized road users. The mutual interactions and diverse bicyclist and pedestrian properties were also incorporated into this model. The mutual interactions were realised through agent spaces of different sizes in conflict and overtaking behaviours for the following combinations: bicyclist-to-pedestrian, bicyclist-to-bicyclist, pedestrian-to-bicyclist, and pedestrian-to-pedestrian, which were obtained through experiments. The hypothesis test indicated that different agent spaces exist for different types of interactions. The experimental data were used to obtain several variables that describe the elements of road user agent spaces, including longitudinal and lateral distances and the dynamic relationship between the longitudinal distance and speed. The simulation results indicated that with an increase in the number of pedestrians, the maximum capacity decreased and the dispersion degree increased. The following psychological and physiological factors affect the degree of dispersion of bicyclists: travelling speed, reaction time, intensity, probability of selecting the head-on direction, and probability of selecting the right-hand direction. In addition, lane formation was observed in all simulations. The results also demonstrated that dedicated bicycle lanes will significantly reduce the dispersion degree. Moreover, the safety and efficiency effects of different forms of bicycle lanes were analysed from the perspective of the degree of dispersion. The simulation results can provide specific guidelines for understanding the causes of phenomena such as dispersion and lane formation, as well as for studying the traffic dynamics, effects of dedicated bicycle lanes, and macroscopic characteristics according to different bicyclist-pedestrian ratios.