We integrate air bubbles into conductive elastic composite-based stretchable conductors to make them mechanically less stiff and electrically more robust against physical deformations. A surfactant facilitates both the formation and maintenance of air bubbles inside the elastic composites, leading to a simple fabrication of bubble-entrapped stretchable conductors. Based on the unique bubble-entrapped architecture, the elastic properties are greatly enhanced and the resistance change in response to tensile strains can clearly be controlled. The bubble-entrapped conductor achieves ~80 % elongation at ~3.4 times lower stress and ~44.8 % smaller change in the electrical resistance at 80 % tensile strain, compared to bare conductor without air bubbles.