This paper proposes a joint multi-task Bayesian channel estimation and data detection algorithm for Turbo equalization (TEQ) in underwater acoustic (UWA) communication. The joint channel estimation and data detection (JCED) problem is formulated as a multi-task sparse Bayesian learning framework in single carrier (SC) communications. The framework treats the equalized symbols as unknown variables for improving the performance of iterative equalization and leverages temporal correlation in UWA channels by partitioning received symbols into subblocks. Furthermore, a JCED algorithm is derived with variational Bayesian inference. The proposed algorithm was evaluated based on the underwater field data collected during a lake experiment conducted in Qiandao Lake, Zhejiang province, China, in May 2016. The performance of the proposed algorithm has been validated with simulation and experiment results.