Orthogonal frequency division multiplexing (OFDM) has been widely adopted in underwater acoustic (UWA) communication due to its good anti-multipath performance and high spectral efficiency. For UWA-OFDM systems, channel state information (CSI) is essential for channel equalization and adaptive transmission, which can significantly affect the reliability and throughput. However, the time-varying UWA channel is difficult to estimate because of excessive delay spread and complex noise distribution. To this end, a novel Bayesian learning-based channel estimation architecture is proposed for UWA-OFDM systems. A clustered-sparse channel distribution model and a noise-resistant channel measurement model are constructed, and the model hyperparameters are iteratively optimized to obtain accurate Bayesian channel estimation. Accordingly, to obtain the clustered-sparse distribution, a partition-based clustered-sparse Bayesian learning (PB-CSBL) algorithm was designed. In order to lessen the effect of strong colored noise, a noise-corrected clustered-sparse channel estimation (NC-CSCE) algorithm was proposed to improve the estimation accuracy. Numerical simulations and lake trials are conducted to verify the effectiveness of the algorithms. Results show that the proposed algorithms achieve higher channel estimation accuracy and lower bit error rate (BER).