For piezoelectric-driven compliant microgrippers, realizing flexible, stable, and accurate manipulation simultaneously is a key challenge. The bridge-type compliant displacement amplification mechanism (CDAM) with a single input force can enable stable parallel grasping and enlarge the grasping stroke by matching the output performance of typical piezoelectric actuators used in microgrippers. In this study, a nonlinear analysis of the bridge-type CDAM with a single input force was conducted to improve the prediction accuracy of the output displacement, and nonlinear optimization and testing were performed. For the expected and parasitic output displacements, a two-step nonlinear modelling method was proposed to conduct the nonlinear analysis. Using Castigliano's second theorem, small deflection-based finite element analysis (FEA), and numerical fitting, small deflection-based modelling considering the shearing effect was first performed. Then, the correction coefficients for the geometrical nonlinearity were modelled by combining geometrical nonlinear FEA and numerical fitting. By restricting the parasitic output displacement, a nonlinear constraint was derived. Thereafter, geometric parameter optimization and structural optimization of the bridge-type CDAM with a single input force was performed. Model analysis indicates that for the optimal CDAM, the expected output displacement increases with the input force, whereas a negative correlation exists between the growth rate and the input force. Finally, simulations and experimental tests were conducted to verify the effectiveness of the nonlinear models, optimization, and model analysis.