In this paper, we use a Bayesian time-varying parameter vector autoregressive (TVP-VAR) model to assess the impact of alternative drivers of bitcoin returns. We consider an extended set of alternative drivers such as bitcoin volatility, investor sentiment indices, proxies for bitcoin supply and demand, stock market returns and volatility indices, commodities returns, exchange rates and interest rates. We select the most important variables using a Bayesian variable selection method. To examine the evolution of the Granger causality relationship between the selected variables and bitcoin returns over time, we develop and employ a new approach based on the estimates of the TVP-VAR model and heteroscedastic consistent Granger causality hypothesis testing. Our findings indicate that investor sentiment and ethereum returns affect bitcoin returns over the entire sampling period. Trading volume emerges as an important determinant of bitcoin returns when bitcoin prices remain relatively steady. In addition to the Granger causality, we perform impulse response function and forecast error variance decomposition analysis. The results from the structural analysis provide further evidence of the time-varying nature of bitcoin’s dynamics. In particular, we find that the effect of a structural shock (in terms of magnitude) on bitcoin returns depends on the time that the shock occurs.