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Because of their momentum-indirect character excitons in bilayer WSe₂ have very long lifetimes, ~ 1ns even at room temperature. They thus play a very important role in the ultrafast dynamics of the system, and hence in the emission spectrum. Details of the ultrafast response that includes the collective role of electrons, holes, excitons and phonons are still unknown. In this study, we present results of our time-dependent density functional theory and many-body theory analysis of the formation of intra- and inter-layer excitons and their dynamics, including the role of inter-layer charge transfer and exciton-exciton interaction in the response of the system. Analysis of the photocurrent and emission spectrum shows that exciton-electron/hole interactions play a significant role in many aspects of the dynamics, while phonons contribute mainly to the inter-valley charge transfer. Furthermore, excitons play an important role in the emission spectrum, resulting in well-pronounced high-harmonic peaks. Our results may contribute to a better understanding of the properties of bilayer transition-metal dichalcogenides and their applications in ultrafast and optical technologies.