Hydraulic bushings exhibit significant amplitude dependent behavior which cannot be captured with the linear time-invariant system theory. Accordingly, Fredette et al. (2016) have proposed a nonlinear model, but the amplitude sensitivity has not been adequately described as it is affected by multiple inherent design features. To further improve the predictive capability of nonlinear models, this article extends the prior work by including two key dissipation effects within the (elastomeric) fluid compliance chambers. First, the conventional fluid compliance element is replaced by an equivalent mechanical spring representing the nonlinear elasticity of the pumping chambers. Fractional calculus based and friction-type damping elements are added in parallel to the nonlinear spring elements of pumping chambers. Second, improved quasi-linear models are proposed at four sinusoidal excitation amplitudes, demonstrating amplitude sensitivity in model parameters. Third, new nonlinear models are proposed and numerically simulated, predicting dynamic stiffness magnitudes and loss angles at multiple excitation amplitudes. The sensitivity of dynamic properties to the fractional and frictional damping parameters is qualitatively evaluated. Finally, both quasi-linear and nonlinear models are experimentally validated and are found to be superior to the ones in the literature.