Dexterous manipulation with world action models (WAMs) relies on hand configuration and contact information, yet joint-state and whole-hand tactile observations may be partially or entirely missing. RGB images provide scene context and hand-object geometry but are insufficient to reliably recover these missing modalities. We further observe a correlation between hand state and tactile information. Motivated by this observation, we introduce BAT-WAM, a framework that bridges visual, joint-state, and tactile representations for WAMs. BAT-WAM learns separate codebooks and decoders for the tactile and action streams. An RGB-conditioned continuous latent bridge connects the two streams for bidirectional learning, while visual information serves as continuous context. Under the HTBench evaluation protocol, BAT-WAM reduces the root mean squared error (RMSE) of tactile reconstruction by 34.73% under fully masked conditions and 38.84% under partially masked conditions, relative to an image-conditioned HandTouch checkpoint. For future tactile prediction conditioned on target-time RGB and historical actions, it reduces mean RMSE by 85.56% relative to OpenWAM with HandTouch. Real-robot experiments further show that BAT-WAM consistently outperforms related WAM baselines in dexterous manipulation. Generalization experiments on unseen objects and scenes also demonstrate substantial improvements over baseline models. These findings support joint modeling of visual context, hand state, and touch as a representation approach for multimodal WAMs.

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