We investigated bubble oscillation and its induced enhancement of mass transfer in a liquid-liquid extraction process with an acoustically-driven, bubble-based microfluidic device. The oscillation of individually trapped bubbles, of known sizes, in microchannels was studied at both a fixed frequency, and over a range of frequencies. Resonant frequencies were analytically identified and were found to be in agreement with the experimental observations. The acoustic streaming induced by the bubble oscillation was identified as the cause of this enhanced extraction. Experiments extracting Rhodanmine B from an aqueous phase (DI water) to an organic phase (1-octanol) were performed to determine the relationship between extraction efficiency and applied acoustic power. The enhanced efficiency in mass transport via these acoustic-energy-assisted processes was confirmed by comparisons against a pure diffusion-based process.