Diffusion processes and random walks describe the dynamics of systems subject to many unpredictable external influences. Here, we show how trajectories of individual ridepooling vehicles are characterized by a novel type of persistent random walk with a preplanned future route. We find three distinct timescales that reflect short- and long-term alignment and medium-term detours emerging in the routing dynamics, together inducing ballistic, subdiffusive, and diffusive motions of the vehicles. The diffusion constant links the timescales underlying the microscopic dynamics of the routes to macroscopic system parameters such as fleet size and effective demand. Observables quantifying the service quality of ridepooling collapse to a single scaling function of the diffusion constant, directly connecting microscopic timescales to macroscopic properties of system operations.