Modeling and analyzing interrelationships within the Bitcoin market, as a prominent cryptocurrency, leads to understanding hidden structures, effective management and informed decision-making. Regarding this matter, numerous studies have analyzed the time-varying spillover patterns in this ecosystem. Although spillover network analysis can elucidate the nature and strength of correlations, it may not be adept at handling the conditional interdependencies within intricate non-linear and dynamic essential behaviors of financial time series. This research tries to address the mentioned challenges by presenting a novel analytical model to investigate the dynamic communication patterns among Bitcoin, United States Economic Policy Uncertainty (US EPU) and public sentiments. Following this objective, rather than directly exploring the effect of original data series on each other, the approach decomposes them into sequences of meaningful statistical behaviors, at different lag-lead horizons. Subsequently, considering the significance of conditional dependencies, we extract and analyze the rules and patterns of information flow among the observed behaviors. The findings not only unveil a distinct flow pattern compared to the spillover network, but also offer valuable insights into dynamic interactions and dominant behaviors under various scenarios. One observation suggests that as the historical range of predictors increases in predicting future changes, their effectiveness or reliability decreases, while their number simultaneously increases. Moreover, the trend slope of Bitcoin functions as a notable behavior in propagating information, directly influencing both economic uncertainty and investor sentiment. The proposed model enhances the understanding of interaction between financial time series and provides useful perspectives for analysis and risk management.