A Cognitive Radio Cloud Network (CRCN) in TV White Spaces (TVWS) is proposed in this paper. Under the infrastructure of CRCN, cooperative spectrum sensing (SS) and resource scheduling in TVWS can be efficiently implemented making use of the scalability and the vast storage and computing capacity of the Cloud. Based on the sensing reports collected on the Cognitive Radio Cloud (CRC) from distributed secondary users (SUs), we study and implement a sparse Bayesian learning (SBL) algorithm for cooperative SS in TVWS using Microsoft's Windows Azure Cloud platform. A database for the estimated locations and spectrum power profiles of the primary users are established on CRC with Microsoft's SQL Azure. Moreover to enhance the performance of the SBL-based SS on CRC, a hierarchical parallelization method is also implemented with Microsoft's dotNet 4.0 in a MapReduce-like programming model. Based on our simulation studies, a proper programming model and partitioning of the sensing data play crucial roles to the performance of the SBL-based SS on the Cloud.