It is known that in addition to spectrum sparsity, spatial sparsity can also be used to further enhance spectral utilization in cognitive radio systems. To achieve that, secondary users (SUs) must know the locations and signal strength distributions (SSDs) of primary users' base stations (PUBSs). Recently, a group sparse total least squares method was developed to cooperatively sense the PUBSs' signal strength and estimate their locations. It approximates PUBSs' power decay with a path loss model (PLM), assumes PUBSs' locations on some grid points, and then accomplishes the estimation tasks. However, the parameters of the PLM have to be known in advance, and the accuracy of the location estimation is bounded by the resolution of the grid points, which limit its practical applications. In this paper, we propose a sparse Bayesian learning method to solve the problems. We use a Laplacian function to model the power decay of a PUBS and then derive learning rules to estimate corresponding parameters. The distinct features of the proposed method are that most parameters are adaptively estimated, and little prior information is needed. To further enhance the performance, we incorporate source number detection methods in the proposed algorithm such that the number of the PUBSs can be precisely detected, facilitating the estimation of PUBSs' locations and SSDs. Moreover, the proposed algorithm is modified into a recursive mode to adapt to SUs' mobility and time-variant observations. Simulations show that the proposed algorithm has good performance, even when the spatial measurement rate is low.