Keyes' model for the electronic contribution to the elastic constants has been extended to the rhombohedral group Vb semimetal bismuth, and the magnitude of the effect calculated using parameters taken from the literature. The theory predicts that an increase in the free electron density should decrease C₁₁, C₆₆ and C₄₄ and increase C₁₂ and C₁₄. These predictions have been tested by measuring the elastic constants of single crystals of bismuth heavily donor-doped with tellurium (10¹⁹-10²⁰ electrons cm^-3); the experiments were performed between 4.2K and room temperature by the ultrasonic pulse echo overlap technique. In general, doping of bismuth with tellurium causes the expected decrease in the ultrasonic wave velocities and the elastic constants vary in the manner predicted by the theoretical model. An increase in the free electron concentration causes C₁₁ and C₆₆ to decrease, C₁₂ to increase, while the variation of C³³ is negligible.