Although cooperative robots have been rapidly introduced in warehouses, high turnover remains a major problem in semi-automated warehouses. Order picking is a representative example of a process where interaction between an automated guided vehicle (AGV) and an operator (picker) could disrupt the work pace of the worker and induce mental stress. Most studies have focused on physical stress, and few have addressed dynamic changes and individual differences in mental stress caused by AGV–picker interactions. This study experimented with the order picking process that incorporates interaction with AGVs by providing a voice notification regarding the number of shelves waiting in front of the workstation (WS) and shelf transfer delay to address this gap. A dynamic Bayesian network (DBN) was used to predict mental stress levels assessed by the picker after processing each order. Further, this study constructed group-specific DBNs for groups with high and low scores on the Big Five factors strongly related to robot acceptance (extraversion, agreeableness, and openness) to address individual differences in stress. The main finding revealed that mental stress levels were higher when the number of shelves waiting in front of the WS was greater or when delays occurred in transporting shelves; further, they were higher for workers with lower levels of extraversion, agreeableness, and openness. The DBN achieved the highest accuracy (0.758) compared to those of three conventional machine learning methods. In addition, the overall accuracy of the DBN (0.768), which was divided into groups with high and low agreeableness scores, exceeded this value.