A data-driven ultimate boundedness controller for a nonlinear system is proposed. The controller is designed based on the inverse model of the system identified by Gaussian process regression with state/input measurement data to track a reference trajectory suitable for achieving a desired ultimate bound. In particular, a suitable reference trajectory is actively generated based on the data that have been used for the identification. For this reason, the controller is named the path generating inverse Gaussian process regression (PGIGP) controller. We provide a sufficient condition on the data under which the PGIGP controller guarantees ultimate boundedness with a desired ultimate bound. It is shown that the condition can serve as a practical guideline for data acquisition and, conversely, be employed to determine the baseline of the control performance achievable from a given dataset. The effectiveness of the PGIGP controller is demonstrated through numerical simulations.