Electroencephalography (EEG)-based P300 brain-computer interfaces (BCIs) enable communication without physical movement by detecting stimulus-evoked neural responses. Accurate and efficient decoding remains challenging due to high dimensionality, temporal dependence, and complex interactions across EEG channels. Existing approaches often treat channels independently or rely on black-box models, limiting interpretability and personalization. We propose a sparse Bayesian time-varying regression framework that explicitly models pairwise EEG channel interactions while performing temporal feature selection, where a relaxed-thresholded Gaussian process prior induces structured sparsity in both channel-specific and interaction effects, enabling interpretable identification of task-relevant channels and channel pairs. Applied to a public P300 speller dataset of 55 participants, our method achieves a 96.4% median character-level accuracy using all sequence repetitions and attains the best overall decoding performance among competing statistical and deep learning approaches. Incorporating channel interactions yields subgroup-specific gains in character-level accuracy, particularly among participants abstained from alcohol (median 7%, up to 14%). Importantly, our approach improves median BCI-Utility by more than 10% at its optimal operating point, achieving peak throughput after only six sequence repetitions. These results demonstrate that explicitly modeling structured EEG channel interactions within a principled Bayesian framework enhances accuracy and user-centric throughput, and supports personalization in P300 BCI systems.

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