Efficient and sustainable bike-sharing service (BSS) operations require accurate demand forecasting for bike inventory management and rebalancing. Probabilistic forecasting provides a set of information on uncertainties in demand forecasting, and thus it is suitable for use in stochastic inventory management. Our research objective is to develop probabilistic time-series forecasting for BSS demand. We use an RNN–LSTM-based model, called DeepAR, for the station-wise bike-demand forecasting problem. The deep-learning structure of DeepAR captures complex demand patterns and correlations between the stations in one trained model; therefore, it is not necessary to develop demand-forecasting models for each individual station. DeepAR makes parameter forecast estimates for the probabilistic distribution of target values in the prediction range. We apply DeepAR to estimate the parameters of normal, truncated normal, and negative binomial distributions. We use the BSS dataset from Seoul Metropolitan City to evaluate the model’s performance. We create district- and station-level forecasts, comparing several statistical time-series forecasting methods; as a result, we show that DeepAR outperforms the other models. Furthermore, our district-level evaluation results show that all three distributions are acceptable for demand forecasting; however, the truncated normal distribution tends to overestimate the demand. At the station level, the truncated normal distribution performs the best, with the least forecasting errors out of the three tested distributions.