The tourism sector, with its perishable nature of products, requires precise estimation of demand. To this effect, we propose a deep learning methodology, namely Bayesian Bidirectional Long Short-Term Memory (BBiLSTM) network. BiLSTM is a deep learning model, and Bayesian optimization is utilized to optimize the hyperparameters of this model. Five experiments using the tourism demand data of Singapore are conducted to ascertain the validity and benchmark the proposed BBiLSTM model. The experimental findings suggest that the BBiLSTM model outperforms other competing models like Long Short-Term Memory (LSTM) network, Support Vector Regression (SVR), Radial Basis Function Neural Network (RBFNN) and Autoregressive Distributed Lag Model (ADLM). The study contributes to tourism literature by proposing a superior deep-learning method for demand forecasting.