This paper presents a Bayesian approach for active tactile exploration of a planar shape in the presence of both localization and shape uncertainty. The goal is to dock the robot’s end-effector against the shape – reaching a point of contact that resists a desired load – with as few probing actions as possible. The proposed method repeatedly performs inference, planning, and execution steps. Given a prior probability distribution over object shape and sensor readings from previously executed motions, the posterior distribution is inferred using a novel and efficient Hamiltonian Monte Carlo method. The optimal docking site is chosen to maximize docking probability, using a closed-form probabilistic simulation that accepts rigid and compliant motion models under Coulomb friction. Numerical experiments demonstrate that this method requires fewer exploration actions to dock than heuristics and information-gain strategies.