An equilibrium network design model is formulated to determine the optimal configuration of a bicycle sharing system in Washington, D.C. Such systems involve a fleet of bicycles positioned at various stations across the network. A user is permitted to check out a bicycle at any station and return it to a station close to her destination. Operators of such systems need to determine the optimal configuration that maximizes utilization. Users employ shared-bicycles for their trips only if their travel utilities improve through their use. An equilibrium approach results in a design that supports the flows it attracts. The model takes the form of a bi-level, mixed-integer program that has a non-convex feasible region. A metaheuristic solution scheme is developed to overcome the intractability of exact solution methods for large networks. System usage patterns and travel time improvements through the use of bicycle sharing are estimated.