Bayesian learning aided massive antenna array based THz MIMO systems are designed forspatial-widebandandfrequency-widebandscenarios, collectively termed as thedual-widebandchannels. Essentially, numerous antenna modules of the THz system result in a significant delay in the transmission/ reception of signals in the time-domain across the antennas, which leads to spatial-selectivity. As a further phenomenon, the wide bandwidth of THz communication results in substantial variation of the effective angle of arrival/ departure (AoA/ AoD) with respect to the subcarrier frequency. This is termed as thebeam squint effect, which renders the channel state information (CSI) estimation challenging in such systems. To address this problem, initially, a pilot-aided (PA) Bayesian learning (PA-BL) framework is derived for the estimation of the Terahertz (THz) MIMO channel that relies exclusively on the pilot beams transmitted. Since the framework designed can successfully operate in an ill-posed model, it can verifiably lead to reduced pilot transmissions in comparison to conventional methodologies. The above paradigm is subsequently extended to additionally incorporate data symbols to derive a Data-Aided (DA) BL approach that performs joint data detection and CSI estimation. We will demonstrate that it is capable of improving the dual-wideband channel’s estimate, despite further reducing the training overhead. The Bayesian Cramér-Rao bounds (BCRLBs) are also obtained for explicitly characterizing the lower bounds on the mean squared error (MSE) of the PA-BL and DA-BL frameworks. Our simulation results show the improved normalized MSE (NMSE) and bit-error rate (BER) performance of the proposed estimation schemes and confirm that they approach their respective BCRLB benchmarks.