Bus operators plan the dispatching times of their daily trips based on the average values of their travel times. Given the trip travel time uncertainty though, the performance of the daily operations is different than expected impacting the service regularity and the expected waiting times of passengers at stops. To address this problem, this work develops a model that considers the travel time uncertainty when planning the dispatching times of trips. In addition, it introduces a minimax approach combining Monte Carlo evaluations with a Genetic Algorithm for computing dispatching times which are robust to travel time variations. This approach is tested in a circular bus line of a major bus operator in Asia Pacific (APAC) using 4 months of Automated Vehicle Location (AVL) and Automated Fare Collection (AFC) data for analyzing the travel time uncertainty and computing robust dispatching times. In addition, 1 month of data is used for validation purposes demonstrating a potential service regularity improvement of 5.5% in the average case and ≃22% in worst-case scenarios.