To minimize the operation time, mobile manipulators need to pick-up parts while the mobile base and the gripper are moving. The gripper speed needs to be selected to ensure that the pick-up operation does not fail due to uncertainties in part pose estimation. This, in turn, affects the mobile base trajectory. This paper presents an active learning based approach to construct a meta-model to estimate the probability of successful part pick-up for a given level of uncertainty in the part pose estimate. Using this model, we present an optimization-based framework to generate time-optimal trajectories that satisfy the given level of success probability threshold for picking-up the part.