Warm dense matter (WDM) is characterized as having temperatures above about 11 605 K and roughly solid densities. Occupying a region in phase space somewhere between hot, sparse plasmas and cool, condensed matter, WDM conditions exist within astrophysical objects, and are created for fractions of a second in inertial confinement fusion (ICF) and laboratory astrophysics experiments. Furthermore, designing and interpreting results from high energy density (HED) laboratory experiments often relies on simulating the complex plasma and material evolution with sophisticated radiation- or magneto- hydrodynamics (R/MHD) codes. In turn, the accuracy of R/MHD simulations rely on detailed descriptions of the material properties like transport coefficients, stopping powers, scattering and absorption spectra, and many other quantities in the WDM regime. However, competing physical effects, like partial ionization, correlated ion behavior, and quantum degeneracy makes model- ing WDM challenging and often computationally expensive. In this thesis, we develop efficient approximate-physics models to describe the unbound, free-electron behavior for WDM. We rely on the dielectric formalism, an approach that has historically been used in this field and show how it can be modified by incorporating electron-ion collision rates from a self-consistent average atom model (AA). We focus on two quantities of interest in the WDM and HED communities: the plasmon peak in the dynamic structure factor (DSF), which can be observed in x-ray Thomson scattering experiments; and the electronic stopping power, which is important for self-heating in ICF. Our results indicate that using collision rates that account for inelastic and strong scattering interactions, ion-ion correlations, and a non-ideal density of states greatly improves agreement with experiments and ab initio theories versus the commonly used Born-based collision theories. Finally, we explore the use of Bayesian statistics to infer dynamic collision rates based on first-principles DSF data, which can qualitatively inform the collisional theories implemented in the AA model. We also show how these methods can use DSF data to bound fundamental transport quantities that are difficult to measure experimentally, like the zero-frequency (DC) electrical conductivity, but find that even in a noise-free case, these bounds are over an order-of-magnitude wide.