Underwater acoustic (UWA) channel estimation holds a pivotal role within in the realm of substantial efforts to improve UWA communication. Conventional adaptive UWA channel estimation techniques, relying on adaptive filtering algorithms, exhibit limited efficacy in scenarios characterized by significant performance degradation under the adverse conditions of time variations, low signal-to-noise (SNR) or large multipath delay spread. In this paper, inspired from the established concept of bidirectional channel equalization, which explores the diversity of two directions to address error propagation caused by feedback decision structure. We propose an innovative variant of the adaptive filtering algorithm by simultaneously harnessing both the bidirectional diversity inherent in twodirectional adaptive filter via joint iteration. To be specific, our proposed algorithms take cognizance bidirectional conjunction in two ways, i.e., leveraging their time-reversal (TR) relationship and strong correlation in terms of similar multipath structure, while alleviating the impact of random interference from the perspective of bidirectional combination. Moreover, we combine the coefficients of the forward and the reverse adaptive filters and feedback to each unidirectional adaptive filter serving as iterative initial. This process yields a bidirectional joint iteration adaptive filtering framework, which can be seamlessly integrated with the conventional adaptive filtering algorithms such as least mean square (LMS) or recursive least square (RLS). Furthermore, we undertake a rigorous theoretical derivation of optimal weight factors for both the forward and reverse directions, thereby enabling us to effectively exploit the diversity gains. We also furnish theoretical models elucidating the transient behavior of the proposed bidirectional joint iteration adaptive filtering algorithms. Both simulation and field experiment results corroborate the superior channel estimation performance exhibited by our proposed bidirectional joint iteration adaptive filtering algorithms in comparison to traditional algorithms, particularly in the challenging time-varying, impulsive noise and low SNR scenarios.