In this paper, we propose power budget allocation algorithms for bidding of auctions in cooperation-based spectrum leasing. The cooperation-based spectrum leasing allows secondary users to dynamically access licensed bands while providing the benefit of cooperative diversity to primary users as a reward. For efficient allocation of the licensed bands to the secondary users, a second-price based multiple auction mechanism is considered. In this mechanism, the secondary users select bands which they want to use and calculate bids for those bands, under a limited transmit power. For the optimal solution of the bidding problem, however, computational complexity increases exponentially with the number of bands. To overcome this problem, we find feasibility conditions for band selection and propose a suboptimal algorithm. The suboptimal algorithm makes bids consisting of the maximum achievable rates for cooperative transmissions. Simulation results show that the primary and secondary users achieve significantly increased achievable rates through spectrum leasing with the proposed algorithms. It is also shown that the performance of the suboptimal algorithm approaches that of the optimal solution as the invested power budget increases.