Coherent jamming severely degrades the performance of adaptive beamforming, particularly under dynamic conditions where the jammer exhibits mobility and only limited stable snapshots are available. Existing methods predominantly rely on static or quasi-static assumptions and struggle to efficiently acquire accurate jamming characteristics from insufficient snapshots. Limited samples lead to ill-conditioned covariance matrix estimates, causing jamming suppression failure. To address this challenge, this paper develops a framework combining covariance matrix reconstruction and null widening. First, leveraging the sparsity of incoming signals, we employ a sparse Bayesian learning (SBL) approach with Jeffreys prior distribution to estimate signal directions-of-arrival (DOA) and power. The Jeffreys prior exhibits a sharp peak at zero, which automatically suppresses power at directions without signals. This suppression thereby ensures spatial sparsity and enabling robust parameter estimation even with insufficient snapshots. Subsequently, an off-grid error correction is performed by maximizing a cost function within a small neighborhood around each coarse estimate. Based on the estimated jamming DOAs and power extracted from potential jamming regions, the jamming-plus-noise covariance matrix (JNCM) is reconstructed to compute adaptive beamforming. This JNCM-based adaptive beamforming can suppress coherent jamming even with a limited number of snapshots under dynamic conditions. Finally, a flexible covariance matrix tapering technique is applied against dynamic jamming, which enables on-demand null widening based on jamming movement patterns. It allows tracking of mobile jammers without repeated weight vector updates or the consumption of additional degrees of freedom. Simulation results under both static and dynamic scenarios demonstrate that the proposed method achieves a superior output signal-to-jamming-plus-noise ratio (SJNR), even in the challenging single-snapshot case.