Service robotics is a fast-developing sector, requiring embedded intelligence into robotic platforms to interact with the humans and the surrounding environment. One of the main challenges in the field is robust and versatile manipulation in everyday life activities. An appealing opportunity to solve the mentioned task is to leverage on machine learning algorithms to let the robot adapt its behavior to unknown scenarios, defining the best strategy for a grasping and manipulation task in a trial and error process. In parallel, the mechanical design of compliant end-effectors able to adapt to the environment targets the same goal. These grippers represent a clever solution to the problems that arise when using sensorized hands with a high number of actuated joints, which are expensive and difficult to control. Within the described context, this work addresses the problem of finding the best position and joint configuration for a compliant, under-actuated, sensorless robotic hand to grasp an unforeseen deformable object based on collected RGB image and partial point cloud. A Bayesian approach to the problem of the optimization of the grasping strategy is proposed, enhancing it with transfer learning capabilities to exploit the acquired grasping knowledge to (partially) new objects. A PAL Robotics TIAGo (a mobile manipulator with a 7-degrees-of- freedom arm and an anthropomorphic underactuated compliant hand) has been used as a test platform, executing a pouring task while manipulating plastic (i.e., compliant) bottles. The sampling efficiency of the data-driven learning is shown, compared to an evenly spaced grid sampling of the input space. In addition, the generalization capability of the optimized model is tested (exploiting transfer learning) on a set of plastic bottles and other liquid containers, achieving a success rate of the 88%.