A recently framed quantum/semiclassical treatment for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium (Chapman, C. T.; Cina, J. A. J. Chem. Phys. 2007,127, 114502) is further analyzed and, subjected to initial tests of its numerical implementation. In the illustrative context of a 1D system interacting with a 1D medium, we rederive the fixed vibrational basis/Gaussian bath (FVB/GB) equations of motion for the parameters defining the Gaussian bath wave packet accompanying each of the energy eigenkets of the quantum mechanical system. The conditions of validity for the Gaussian-bath approximation are shown to coincide with those supporting approximate population conservation. We perform initial numerical tests of;the FVB/GB scheme and illustrate the semiclassical description it provides of coherent motion in the medium by comparing its predictions with the exact results for a high-frequency system harmonic oscillator bilinearly coupled to a lower-frequency bath oscillator. Linear vibronic absorption spectra or, equivalently, ultrafast wave packet interferometry signals are shown to be readily and accurately calculable within the FVB/GB framework.