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The staggered work hours (SWH) policy is a practical strategy for managing travel demand, aiming to spread out the temporal distribution of travel volume by adjusting the schedules of travelers' activities. The influence of the SWH policy on the commuting patterns of passengers using bus transit is not yet clear. We addressed this issue in a many-to-one bus line, treating commuters as Q-learning agents learning to minimize regrets by selecting appropriate bus runs. The learning outcomes reveal a SWH-induced equilibrium, where commuters departing from the same station with the same work start time experience identical minimal commuting costs, regardless of the chosen bus. Subsequently, we investigate the effectiveness of SWH policy by manipulating two key control variables: the division of travel demand between two categories of travelers and the staggered time interval. The results confirm that congestion during peak hours can potentially be mitigated by carefully selecting the above two key parameters. Correspondingly, we provide optimal control boundaries for these two parameters to design an effective SWH policy. Furthermore, we explore the combined impact of physical distancing and SWH policy on traffic flow patterns during an epidemic outbreak. Concurrently, we assess the infection risk through a surrogate index, revealing that the SWH policy has a positive effect in mitigating the risk of contact exposure. [ABSTRACT FROM AUTHOR]