Ultrasound is a vital imaging modality utilized for a variety of diagnostic and interventional procedures. However, an expert sonographer is required to make accurate maneuvers of the probe over the human body while making sense of the ultrasound images for diagnostic purposes. This procedure requires a substantial amount of training and up to a few years of experience. In this paper, we propose an autonomous robotic ultrasound system that uses Bayesian Optimization (BO) in combination with the domain expertise to predict and effectively scan the regions where diagnostic quality ultrasound images can be acquired. The quality map, which is a distribution of image quality in a scanning region, is estimated using Gaussian process in BO. This relies on a prior quality map modeled using expert's demonstration of the high-quality probing maneuvers. The ultrasound image quality feedback is provided to BO, which is estimated using a deep convolution neural network model. This model was previously trained on database of images labelled for diagnostic quality by expert radiologists. Experiments on three different urinary bladder phantoms validated that the proposed autonomous ultrasound system can acquire ultrasound images for diagnostic purposes with a probing position and force accuracy of 98.7% and 97.8%, respectively.