Ice sheets are expected to be major contributors to sea level rise in the coming decades and centuries. Ocean-forced melting at marine terminating glaciers has the potential to be an important driver of mass loss from these ice sheets, but is difficult to measure directly using conventional techniques, and thus remains poorly understood. The air pressure in bubbles trapped in glacier ice is typically greater than the hydrostatic pressure near the surface of the water. This pressure difference causes the bubbles to expand rapidly and radiate sound when they are released as the ice melts. This sound presents a promising signal which could be used to make passive acoustic measurements of submarine melting at glacier termini, if it can be characterized sufficiently. Prior work has demonstrated that there is considerable variability in the acoustic energy radiated by the release of individual bubbles. Here we show that the total acoustic energy radiated by small blocks of glacier ice as they melt is correlated with the total potential energy stored by the compressed air bubbles in the ice. We find that the conversion efficiency is highest for the most energetic blocks of ice, and present some modelling efforts to explain this trend.