Hydraulic bushings are typically characterized in terms of sinusoidal dynamic stiffness at lower frequencies over a range of excitation amplitudes. However, in practice they are also exposed to severe transient loads in conjunction with sinusoidal excitations. Three improved nonlinear, lumped parameter models for hydraulic bushings are developed with the goal of concurrently predicting amplitude-sensitive dynamic responses to both sinusoidal and step-like excitations using a common dynamic model with the same parameters. First, a fluid resistance element is introduced which extends previous formulations by relaxing the assumption of fully developed turbulent flow, and capturing the transition from laminar flow to turbulence. Second, a bleed orifice element between the two compliance chambers is incorporated to simulate leakage observed in laboratory testing. The sensitivity of the dynamic responses to linearized model parameters is used to guide the parameter identification procedure. Measured dynamic stiffness spectra and step-like responses provide experimental validation of the proposed formulations. The new formulations achieve improved predictions of dynamic stiffness or force using exactly the same set of model parameters at several excitation amplitudes in both time and frequency domains.