Quantum logic gates based on quantum electrodynamics (QED) in strong coupling regime between quantum dots and microcavities are key elements for scalable quantum computing and all-optical quantum networks. Here, a single colloidal quantum dot was site-selectively positioned onto a dielectric photonic crystal hybrid microcavity using a soft nanoprobe technique, enabling the study of strong coupling between the colloidal quantum dots and bound states in the continuum in the cavity. By combining photoluminescence spectroscopy, Michelson interferometry, and continuous-wave pump-probe technology, the wavelength- and power-dependent phase shifts were systematically characterized. Controlled π-phase shifts of a single photon were experimentally demonstrated in both single colloidal quantum dot and high-concentration colloidal quantum dots coupled microcavity systems. This work provides an experimental basis for the development of room temperature quantum optoelectronic devices, including quantum phase gates and ultralow power optical switches.