Using a parsimonious model, this paper analyzes a dockless bike-sharing (DLB) service that competes with walking and a generic motorized mode. The DLB operator chooses a fleet size and a fare schedule that dictate the level of service (LOS) as measured by the access time or the walking time taken to reach the nearest bike location. The market equilibrium is formulated as a solution to a nonlinear equation system over which three counterfactual design problems are defined to maximize (i) profit, (ii) ridership, or (iii) social welfare. The model is calibrated with empirical data collected in Chengdu, China, and all three counterfactual designs are tested against the status quo. We show the LOS of a DLB system is subject to rapidly diminishing returns to the investment on the fleet. Thus, under the monopoly setting considered herein, the current fleet cap set by Chengdu can be cut by up to three quarters even when the DLB operator aims to maximize ridership. This indicates the city’s fleet cap decision might have been misguided by the prevailing conditions of a competitive yet highly inefficient market. For a regulator seeking to influence the DLB operator for social good, the choice of policy instruments depends on the operator’s objective. When the operator focuses on profit, limiting fare is much more effective than limiting fleet size. If, instead, it aims to grow market share, then setting a limit on fleet size becomes a dominant strategy. We also show, both analytically and numerically, that the ability to achieve a stable LOS with a low rebalancing frequency is critical to profitability. A lower rebalancing frequency always rewards users with cheaper fares and better LOS even for a profit-maximizing operator.