This paper proposes a public transport users’ scheduling model that considers crowding inside vehicles, waiting time, and punctuality as a reliability measure. Commuters simultaneously make two choices: the preferred bus and the timing to arrive at the bus stop (on time or late). Public transport punctuality is the probability of being on time or late, generating a parameter of public transport reliability. We compute users’ equilibrium, social optimum, and first-best pricing and analytically devise a methodology to obtain the second-best pricing. Using numerical analysis, we show that (i) punctuality plays an essential role in the commuter strategy modifying according to its level, (ii) commuters’ strategy changes according to how reliable the system is, and (iii) second-best pricing is efficient only for limited cases.