Smart Mobility is the key component of Smart City initiative that are being explored throughout the world. The bikesharing system (BSS) aims to provide an alternative mode of Smart Mobility transportation system, and it is being widely adopted in urban areas. The use of bikes for short-distance travel helps to reduce traffic congestion, reduce carbon emissions, and decrease the risk of overcrowding. Effective bike sharing system operations requires rebalancing analysis, which corresponds to transferral of bikes across various bike stations to ensure the supply meets expected demand. A critical part for a bike sharing system operations is the effective management of rebalancing vehicle carrier operations that ensures bikes are restored in each station to its target value during every pick-up and dropoff operations. In this work, we present potential applications of Quantum Bayesian networks, which are quantum-equivalent to classical Bayesian networks for probabilistic rebalancing cost prediction under uncertainty. In this preliminary work, we demonstrate the proposed approach using IBM-Qiskit and compared the results classically using Netica for a case study involving rebalancing across three bike stations.