This paper addresses the problem of robust bottom following control for a flight-style autonomous underwater vehicle (AUV) subject to system uncertainties, actuator dynamics, and input saturation. First, the actuator dynamics that is approximated by a first-order differential equation is inserted into the AUV dynamics model, which renders a high-order nonlinear dynamics analysis and design in the model-based backstepping controller by utilizing guidance errors. Second, to overcome the shaking control behavior resulted by the model-based high-order derivative calculation, a fuzzy approximator-based model-free controller is proposed, in order to online approximate the unknown part of the ideal backstepping architecture. In addition, the adaptive error estimation technology is resorted to compensate the system approximation error, ensuring that all the position and orientation errors of robust bottom following control tend to zero. Third, to further tackle the potential unstable control behavior from inherent saturation of control surfaces driven by rudders, an additional adaptive fuzzy compensator is introduced, in order to compensate control truncation between the unsaturated and saturation inputs. Subsequently, Lyapunov theory and Barbalat lemma are adopted to synthesize asymptotic stability of the entire bottom following control system. Finally, comparative numerical simulations with different controllers, environmental disturbances and initial states are provided to illustrate adaptability and robustness of the proposed bottom following controller for a flight-style AUV with saturated actuator dynamics.