Taking advantage of the merits of both the bootstrap-aggregating method and the Bayesian forecasting approach, this study introduces their combination—the BayesBag method—to the tourism forecasting literature for the first time. In this study, we examine whether the novel BayesBag method can improve the forecasting performance of the traditional Autoregressive-Distributed-Lag (ADL) model in both normal (i.e., pre-COVID-19) and crisis (i.e., during the pandemic) times. This is also the first study to incorporate the global travel sentiment index as a measure of visitors’ behavioral intentions for forecasting tourism demand in a crisis situation. We conduct both ex-post and ex-ante forecasting of European monthly tourism demand, and our empirical results show that the newly proposed BayesBag method outperforms other methods in both periods.