This paper addresses the application of the emerging compressive sensing (CS) technology to the detection of ultra-wideband (UWB) signals. Capitalizing on the sparseness of random UWB signals in the basis of eigen-functions, we develop a new CS dictionary called eigen- dictionary. Coupled with this eigen-dictionary, an enhanced Bayesian learning procedure is proposed to reconstruct the sparse UWB signal from a small collection of random projection measurements. Furthermore, by utilizing a common sparsity profile inherent in UWB signals, the proposed Bayesian algorithm naturally lends itself to multi-task CS for simultaneously recovering multiple UWB signals. Since the statistical inter-relationships between different CS tasks are exploited, the multi-task (MT) Bayesian CS can efficiently improve the reconstruction accuracy and thus the performance of UWB communications. Simulations based on real UWB data demonstrate the advantages of the proposed approach over its counterparts.