Oxide glasses with the general formula (Bi2O3)(1-x)(CuO)(x) have been prepared by quick quenching technique. Their longitudinal and shear elastic moduli have been determined by measuring the corresponding ultrasonic wave velocities between 300 and 470 K, which are well below the glass transition temperature of this system. Temperature variation of ultrasonic velocity and attenuation exhibit anomalies around 435 K in glasses with x greater than or equal to 0.3. A nonlinear behaviour is also reflected in the CuO concentration dependent dielectric constant curve around x = 0.3. These anomalies are interpreted in terms of a structural softening (or transformation) taking place in samples having CuO concentration above the critical value. The high dielectric constant of these glasses show very little increase with increase of temperature. Anomalies are also found in the temperature dependence of dielectric constant around 435 K. This behaviour is again considered to be associated with the softening of the glass network.