Modelling of bike sharing systems as Markov Renewal Process is examined with the aim of capturing and assessing various forms of user (dis)satisfaction. A class of models with minimal assumptions about distributions of bicycle parking stations and service requests is developed in which rational commuter behaviour is taken into account. Stochastic time evolution of these models is studied, using a generalised version of Gillespie's exact stochastic integration algorithm that accounts for non-Markovian inter-event times. The model is shown to reproduce quite faithfully the trip-duration statistics of smaller and larger real bike sharing systems, such as those in London and Pisa, including the algebraic `tails' of these distributions that are made up of longer cycling trips. The latter are related to user's difficulties to find suitable parking places therefore to a potential source of distress. The model also predicts other salient features such as a mode at 10 minutes and crossover behaviour at about 30 minutes. The framework can be extended to include measures either designed to improve, or anyway to affect, the user experience with a system, such as incentives for spontaneous vehicle redistribution. User satisfaction is difficult to assess in real systems because these naturally collect only data about trips that actually, and thus successfully, took place giving only partial and biased insight in user satisfaction.