The application of compressive sensing (CS) theory has found great interest in wideband spectrum sensing. Although most studies have considered perfect reconstruction of the primary user signal, it is actually more important to assess the presence or absence of the signal. Among CS based methods, Bayesian CS (BCS) takes into consideration the prior information of signal coefficients to be estimated, which improves signal reconstruction performance. On the other hand, the sparsity level of the signal to be estimated has a direct impact on signal reconstruction and detection performances. Considering all of the above, the effect of sparsity level on BCS based spectrum sensing is studied in this paper. More specifically, a BCS based spectrum sensing scheme is considered and its mean-square error (MSE) performance is compared with the Bayesian Cramer-Rao bound for various user bandwidths. BCS MSE is also compared with the deterministic lower MSE (DL-MSE), which is a tight lower bound of the conventional basis pursuit approach. Furthermore, complementary receiver operating characteristic (ROC) curves are obtained to examine the trade-off between probabilities of false alarm and detection, depending on the user signal bandwidth.