The principle of “first-come-first-served” (FCFS) has been widely adopted in the deployment of car-sharing services (CSS) to manage service requests for the sake of equity. Most studies of CSS do not explicitly model the supply-demand interactions of shared cars, especially when supply insufficiency arises. This study formulates the supply-demand dynamics of one-way CSS under different FCFS mechanisms and embeds them in a boundedly rational dynamic user equilibrium (BR-DUE) problem. Two disaggregate FCFS mechanisms are suggested to improve the utilization of shared cars given the same CSS supplies in the discrete-time domain. To accurately capture the choice of CSS in space and time, a path expansion strategy is proposed to cope with different waiting times under the disaggregate FCFS mechanisms. The path expansion strategy congruently bridges the aggregate-disaggregate analyses and is incorporated in an adaptive column generation algorithm to solve the BR-DUE problem in a bi-modal supernetwork. Numerical examples demonstrate that the FCFS mechanisms have a significant influence on the supply-demand dynamics and choice of CSS.