We report on the first observation of multiple-order bistability due to acoustic radiation pressure in a compliant acoustic cavity formed between a spherical ultrasonic transducer immersed in water and the free liquid surface located at its focus. The hysteretic behavior of the cavity length, observed both with amplitude ramps and frequency sweeps, is accurately described using a one-dimensional model of a compliant Fabry-Pérot resonator assuming the acoustic radiation pressure to be the only coupling between the cavity and the acoustic field.