Bodily gestures play an important role in joint musical interactions. In a series of empirical studies, we investigated how bodily gestures may support an emergent timing mechanism. Results show that gestures can contribute to joint musical timing, in the way they can lower cognitive load and provide cues that facilitate accurate prediction. In a second series of studies, I will present a new empirical protocol to investigate the relationship between the time-varying coordination dynamics of a joint musical interaction, and the subjectively-felt quality of that interaction (related to the sense of joint agency). We adopt thereby a Bayesian inference framework as a guide for our methodological choices. Finally, I will conclude my talk with a brief discussion on ongoing and future research, that employs virtual reality as a methodological framework to study fundamental aspects of embodied music interaction.