We consider a network inventory system motivated by one-way, on-demand vehicle sharing services. Under uncertain and correlated network demand, the service operator periodically repositions vehicles to match a fixed supply with spatial customer demand while minimizing costs. Finding an optimal repositioning policy in such a general inventory network is analytically and computationally challenging. We introduce a base-stock repositioning policy as a multidimensional generalization of the classical inventory rule to $n$ locations, and we establish its asymptotic optimality under two practically relevant regimes. We present exact reformulations that enable efficient computation of the best base-stock policy in an offline setting with historical data. In the online setting, we illustrate the challenges of learning with censored data in networked systems through a regret lower bound analysis and by demonstrating the suboptimality of alternative algorithmic approaches. We propose a Surrogate Optimization and Adaptive Repositioning algorithm and prove that it attains an optimal regret of $O(n^{2.5} \sqrt{T})$, which matches the regret lower bound in $T$ with polynomial dependence on $n$. Our work highlights the critical role of inventory repositioning in the viability of shared mobility businesses and illuminates the inherent challenges posed by data and network complexity. Our results demonstrate that simple, interpretable policies, such as the state-independent base-stock policies we analyze, can provide significant practical value and achieve near-optimal performance.