To improve the settling time for high-speed point-to-point motion, a piecewise-model feedforward controller is introduced which utilizes multiple inverse sub-models with bumpless transfer between them. As the transfer function of this bumpless feedforward controller is non-commutative and non-invertible, a set of special perturbation and reference inputs are designed to extract the signals required for computing the gradient of the cost function. In this way, the optimal parameters within different motion phases are found within an integrated process. It is experimentally demonstrated in a wire-bonding machine that the root-mean-square of tracking error is improved by at least 15.3% in settling phase by the proposed data-based tuning method with bumpless feedforward controller, compared with existing tuning methods with uniform feedforward controller.