This letter investigates the performance bounds of sensing and communications (S&C) in perceptive networks, where multiple user equipments (UEs) are deployed with both S&C capabilities whose performances are both closely related to the allocated bandwidth. To this end, we develop a novel bandwidth allocation strategy which optimizes the weighted average range resolution for sensing, while guaranteeing the sum-rate among UEs for wireless communications. We first formulate the bandwidth allocation problem into a convex optimization programming, and then develop a highly efficient algorithm to obtain the optimal solution. Through a deeper analysis of the problem structure, we build an initial understanding and provide insights into the performance tradeoff between S&C, which can be achieved by three specifically tailored bandwidth allocation schemes. Numerical results are given to verify the performance of the proposed method, showing that our bandwidth allocation scheme achieves the pareto boundary of S&C performance, with significantly reduced computational complexity.