Ride sharing - the bundling of simultaneous trips of several people in one vehicle - may help to reduce the carbon footprint of human mobility. However, the complex collective dynamics pose a challenge when predicting the efficiency and sustainability of ride sharing systems. Standard door-to-door ride sharing services trade reduced route length for increased user travel times and come with the burden of many stops and detours to pick up individual users. Requiring some users to walk to nearby shared stops reduces detours, but could become inefficient if spatio-temporal demand patterns do not well fit the stop locations. Here, we present a simple model of dynamic stop pooling with flexible stop positions. We analyze the performance of ride sharing services with and without stop pooling by numerically and analytically evaluating the steady state dynamics of the vehicles and requests of the ride sharing service. Dynamic stop pooling does a priori not save route length, but occupancy. Intriguingly, it also reduces the travel time, although users walk parts of their trip. Together, these insights explain how dynamic stop pooling may break the trade-off between route lengths and travel time in door-to-door ride sharing, thus enabling higher sustainability and service quality.