In this paper, we propose a continuous-time multi-agent system via event-triggered communication among agents for distributed optimization. We develop a dynamic bi-event triggering rule based on both local decision variables and auxiliary variables to reduce communication costs. We design a bi-event triggered multi-agent system based on the Karush-Kuhn-Tucker conditions, which allows initializing auxiliary variables arbitrarily and hence relaxing the existing zero-sum condition on the initial values of auxiliary variables. We prove the exponential convergence of the multi-agent system to the optimal solution and derive a lower bound of the convergence rate. In addition, we prove the capability of the triggering rule for precluding Zeno behavior. We also elaborate on two numerical examples to illustrate the effectiveness and characteristics of the theoretical results.