Smart Mobility is the key component of Smart City initiative that are being explored throughout the world. The bike-sharing 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 transferal 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 drop-off operations. In this work, we compare the performance of two types of quantum optimization algorithms (Quantum Approximate Optimization Algorithm and Quantum Annealing) to evaluate performance of bike sharing rebalancing optimization. In this preliminary work, we compared the performance of QAOA on IBM-Qiskit and Quantum Annealing on two D-Wave solvers (QPU and hybrid solvers) for a case study involving rebalancing across three bike stations.