This paper investigates a novel intelligent reflecting surface (IRS)-based commensal symbiotic radio (CSR) system architecture consisting of a transmitter, an IRS, and an information receiver (IR). The primary transmitter communicates with the IR and at the same time assists the IRS in forwarding information to the IR. We formulate a bit error rate (BER) minimization problem by jointly optimizing the active beamformer at the base station and the phase shifts at the IRS, subject to a minimum primary rate requirement. Since the formulated optimization problem is non-convex with unit-modulus constraints, there are no standard convex techniques to solve it optimally in general. To tackle this difficulty, a penalty-based algorithm is proposed to obtain a high-quality solution, where semi-closed-form solutions for the active beamformer and the IRS phase shifts are derived based on Lagrange duality and Majorization-Minimization methods, respectively. Simulation results demonstrate the effectiveness of the proposed algorithm and show that the proposed CSR technique is able to achieve a lower BER than benchmark schemes.