The bus system offers an eco-friendly mode of travel in contrast to private cars, contributing to reduced carbon emissions and environmental protection. However, some potential passengers find it challenging to use the bus due to a misalignment between bus arrival times and their preferred usage times. For example, passengers opt for alternative modes of travel if the bus doesn’t arrive within their desired departure time window, resulting in unmet bus demand. In this study, we aim to optimize the schedule for the single bus line considering potential passengers’ demand and their uncertain departure time window. The primary objective is to minimize unmet bus demand, with the decision variables including departure and dwell times of buses. To address uncertainty, we establish a stochastic optimization model, which is then transformed into a mixed-integer programming model using the sample average approximation (SAA) and linearization technique. Acknowledging that the SAA approach provides an approximate solution rather than an exact one, we are also interested in reducing the approximation error. To achieve this, Halton draws, a typical quasi-Monte Carlo sampling technique, is adopted. This outcome demonstrates that SAA with Halton draws is more effective and accurate than the standard SAA.