In recent years, bike-sharing systems (BSS) are being widely established in urban cities to provide a sustainable mode of transport, by fulfilling the mobility requirements of public residents. The application of BSS in highly congested urban cities reduces the effect of overcrowding, pollution, and traffic congestion problems. The crucial role behind incorporating BSS depends on the prediction of bike demand across all the bike stations. The bike demand prediction involves real-time analysis for identifying the discrepancy between the bike pick-up and drop-off throughout all the bike stations in a given time period. To enhance the prediction analysis of bike demand we propose quantum computing algorithms to provide computational speedup in comparison with classical algorithms. In this paper, we illustrate the construction of Quantum Bayesian Networks (QBN), for predicting bike demand. Furthermore, we provide a solution framework for implementing QBN for two case studies: (a) bike demand prediction during weekdays, (b) bike demand prediction during weekends. We have compared the quantum and classical solutions, by using IBM-Qiskit and Netica computing platforms.