Aiming at bi-objective optimization problems where gradient information is difficult to obtain or computationally expensive, this paper proposes a bi-objective derivative-free optimization algorithm based on noncommutative maps. The comprehensive gradient descent is approximated only using objective function values in the bi-objective optimization problems. Furthermore, to balance the trade-off between conflicting objectives and prevent over-optimizing some objective, a conflict-corrected bi-objective derivative-free optimization algorithm is proposed by minimizing a modified cost function that incorporates a penalty term and a regularization term. The stability of the proposed algorithm for a class of strongly convex objective functions is proven using Lyapunov functions. Numerical simulations demonstrate that compared to other bi-objective derivative-free optimization algorithms, the proposed algorithm exhibits superior performance in handling conflicting trade-off between objectives. It effectively prevents converging to endpoints of the Pareto front, providing an efficient derivative-free scheme for bi-objective optimization problems when gradient information is unavailable.