The simultaneous sparse approximation problem is concerned with recovering a set of multichannel signals that share a common support pattern using incomplete or compressive measurements. Multichannel modifications of greedy algorithms like orthogonal matching pursuit (OMP), as well as convex mixed-norm extensions of the Lasso, have typically been deployed for efficient signal estimation. While accurate recovery is possible under certain circumstances, it has been established that these methods may all fail in regimes where traditional subspace techniques from array processing, notably the MUSIC algorithm, can provably succeed. Against this backdrop several recent hybrid algorithms have been developed that merge a subspace estimation step with OMP-like procedures to obtain superior results, sometimes with theoretical guarantees. In contrast, this paper considers a completely different approach built upon Bayesian compressive sensing. In particular, we demonstrate that minor modifications of standard Bayesian algorithms can naturally obtain the best of both worlds backed with theoretical and empirical support, surpassing the performance of existing hybrid MUSIC and convex simultaneous sparse approximation algorithms, especially when poor RIP conditions render alternative approaches ineffectual.