We study information dynamics between the largest Bitcoin exchange markets during the bubble in 2017-2018. By analyzing high-frequency market microstructure observables with different information-theoretic measures for dynamical systems, we find temporal changes in information sharing across markets. In particular, we study time-varying components of predictability, memory, and (a)synchronous coupling, measured by transfer entropy, active information storage, and multi-information. By comparing these empirical findings with several models, we argue that some results could relate to intra-market and inter-market regime shifts and changes in the direction of information flow between different market observables.