Understanding the factors influencing bicycling is important to improve educational and built-environment investments to increase bicycling rates. Although factors such as the physical environment, sociodemographics, and psychology influence bicycling, safety is also one of the primary reasons people avoid bicycling. Interventions based on objective safety can reduce the number of crashes, injuries, and fatalities, but people might still feel uncomfortable bicycling owing to subjective safety (perceived safety or avoidance of risk). Several studies have examined the subjective safety of bicyclists based on stated-preference surveys, but these studies have limitations, including response bias. A revealed preference method was implemented by combining 9,101 bicycling trips of Grid Bike Share in Arizona with transportation network and crash data. A segmented path size correction logit model identified that regular bicyclists took a 1.6-times longer detour to avoid historic crash locations than casual bicyclists. These two groups also exhibited different choices related to the built environment and navigation. The significance of different types of bicyclists avoiding historic crash locations or risky infrastructure is that this indicates that crash datasets coupled with route data could be used as one of several indicators of perceived safety. Recommendations to increase perceived safety and reduce the crash risk of occasional bicyclists include expanding bicycle-specific infrastructure, constructing contraflow bicycle lanes in a one-way street, separating high volume lanes with a bike lane, and improving the education of road users.