We experimentally demonstrated collective strong coupling, optical bistability, and all-optical switching in a system consisting of ultracold ⁸⁵Rb atoms, trapped in a dark magneto-optical trap, and coupled to an optical Fabry-Perot cavity. The collective strong coupling was established by the observation of vacuum Rabi splitting (VRS) in the transmission spectrum of an on-axis weak probe beam. A closer look at VRS measurements done with different probe light intensities showed that VRS decreases with increasing probe intensity. The measurements also revealed an asymmetry in the line shape of the vacuum-Rabi peaks – a signature of optical bistability. When the probe laser is locked to the atomic transition and its power is scanned, the cavity transmission shows bistable behaviour and the cavity input-output curve shows hysteresis. The shape of the hysteresis could be controlled by another off-axis control laser, with a few µW power (P_c ), tuned near a different atomic transition (see figure below). This results from the probe and control beams forming a Λ-type system. We also demonstrated that the cavity transmission can be switched on and off in micro-second timescales using micro-Watt control powers.