Complex systems like human mobility exhibit a wide range of collective dynamics. Ride-sharing, the combination of multiple similar trips into one, is a particularly prominent example due to the complex interplay between the requests and the vehicle fleet. Several contributions have analyzed the dynamics of the routing and the service efficiency of ride-sharing fleets. Here, we adopt a complementary perspective and study the adoption of ride-sharing from the perspective of its users. Collective interactions of the users to avoid detours in shared rides give rise to spontaneous symmetry breaking, pattern formation dynamics, and bistability, potentially limiting the adoption of ridesharing. Our results may provide a framework to understand real-world adoption patterns of ridesharing in complex urban settings and (re)design ride-sharing services and incentives to promote sustainable shared mobility.