In order to guarantee precision and safety in robotic surgery, accurate models of the robot and proper control strategies are needed. Bayesian Neural Networks (BNN) are capable of learning complex models and provide information about the uncertainties of the learned system. Model Predictive Control (MPC) is a reliable control strategy to ensure optimality and satisfaction of safety constraints. In this work we propose the use of BNN to build the highly nonlinear kinematic and dynamic models of a tendon-driven surgical robot, and exploit the information about the epistemic uncertainties by means of a Hierarchical MPC (Hi-MPC) control strategy. Simulation and real world experiments show that the method is capable of ensuring accurate tip positioning, while satisfying imposed safety bounds on the kinematics and dynamics of the robot.