Orthogonal time frequency space (OTFS) as an emerging modulation technique in the 5G and beyond era exploits full time-frequency diversity and is robust against doubly-selective channels in high mobility scenarios. In this work, we consider an OTFS modulation based automotive joint radar-communication system and focus on the design of low-complexity parameter estimation algorithm for radar targets. It is well known that target parameter estimation in OTFS radar is computationally much more expensive than the orthogonal frequency division multiplex based platform, which hampers low-cost and real-time implementation. In this context, an efficient Bayesian learning scheme is proposed for OTFS automotive radars, which leverages the structural sparsity of radar channel in the delay-Doppler domain. We also reduce the dimension of the measurement matrix by incorporating the prior knowledge on the motion parameter limit of the true targets. Numerical simulation results are presented to demonstrate the superior performance of the proposed method in comparison with the state-of-the-art.