In this paper, we propose to use a Nonlinear Adaptive PID controller to regulate the joint variables of a mobile manipulator. Motion of the mobile base forces undue disturbances on the joint controllers of the manipulator. In design of a conventional PID controller a trade-off should be made between the performance and agility of the closed-loop system and its stability margins. Considering the uncertainty and disturbances the controllers of the joints of a mobile manipulator experience, this trade-off must be in favor of increasing the stability margins. The proposed nonlinear adaptive PID controller provides us with a mechanism to relax the need for such a compromise by adapting the gains according to the magnitude of the error. Therefore, we can achieve nimble performance for the system while seeing damped overshoot in the output, and track the reference as close as possible even in the presence of external disturbances and uncertainty in the model of the system. We have employed Bayesian Optimization technique to choose the parameters of the Nonlinear Adaptive PID controller to achieve the best performance in tracking the reference input and rejecting disturbances. The results indicate that a well-designed Nonlinear Adaptive PID controller can effectively regulate the joint variables of a mobile manipulator while it is carrying a heavy load and the base of the robot is maneuvering fast.