  Bike sharing systems have been widely deployed around the world in recent
years. A core problem in such systems is to reposition the bikes so that the
distribution of bike supply is reshaped to better match the dynamic bike
demand. When the bike-sharing company or platform is able to predict the
revenue of each reposition task based on historic data, an additional
constraint is to cap the payment for each task below its predicted revenue. In
this paper, we propose an incentive mechanism called {\em TruPreTar} to
incentivize users to park bicycles at locations desired by the platform toward
rebalancing supply and demand. TruPreTar possesses four important economic and
computational properties such as truthfulness and budget feasibility.
Furthermore, we prove that even when the payment budget is tight, the total
revenue still exceeds or equals the budget. Otherwise, TruPreTar achieves
2-approximation as compared to the optimal (revenue-maximizing) solution, which
is close to the lower bound of at least $\sqrt{2}$ that we also prove. Using an
industrial dataset obtained from a large bike-sharing company, our experiments
show that TruPreTar is effective in rebalancing bike supply and demand and, as
a result, generates high revenue that outperforms several benchmark mechanisms.
