Millimetre-sized droplets are able to bounce multiple times on flat solid substrates irrespective of their wettability, provided that a micrometre-thick air layer is sustained below the droplet, limiting $\mathit{We}$ to ${\lesssim}4$. We study the energy conversion during a bounce series by analysing the droplet motion and its shape (decomposed into eigenmodes). Internal modes are excited during the bounce, yet the viscous dissipation associated with the in-flight oscillations accounts for less than 20 % of the total energy loss. This suggests a significant contribution from the bouncing process itself, despite the continuous presence of a lubricating air film below the droplet. To study the role of this air film we visualize it using reflection interference microscopy. We quantify its thickness (typically a few micrometres) with sub-millisecond time resolution and ${\sim}30~\text{nm}$ height resolution. Our measurements reveal strong asymmetry in the air film shape between the spreading and receding phases of the bouncing process. This asymmetry is crucial for effective momentum reversal of the droplet: lubrication theory shows that the dissipative force is repulsive throughout each bounce, even near lift-off, which leads to a high restitution coefficient. After multiple bounces the droplet eventually hovers on the air film, while continuously experiencing a lift force to sustain its weight. Only after a long time does the droplet finally wet the substrate. The observed bounce mechanism can be described with a single oscillation mode model that successfully captures the asymmetry of the air film evolution.