By making use of the changes in optical properties such as absorption and dispersion around the resonance generated via electromagnetically induced transparency (EIT), we theoretically and experimentally investigate a "∞"-shape optical bistability (OB) versus frequency on the probe transmission with a Λ-shape EIT window in a rubidium atomic ensemble confined in a three-mirror optical ring cavity. Compared to the traditional OB reflected by a hysteresis loop versus power, such newly demonstrated optical bistable behavior (represented by a "∞"-shape non-overlapping region) by scanning probe and cavity detuning can experience dual bistabilities and be more sensitive to the change of experimental parameters. Further, we study the relationship between vacuum Rabi splitting and the "∞"-shape OB. Such study on frequency-induced OB could effectively improve the applications related to OB such as logic-gate devices and optical information processing.