Lithium-sulfur (Li/S) batteries constitute a promising, next-generation energy storage technology due to their high theoretical energy density and low cost. To increase sustainability, processability, and battery performance, conducting organic polymers have become a focus of research for the development of better cathode materials. Here, we investigate the solvation structure of the conjugated poly(4-thiophen-3-yl) benzenethiol) (PTBT) polymer as a high-potential macromolecular candidate for cathodes in Li/S batteries. Using molecular dynamics (MD) simulation with newly optimized force-field parameters, we examine the effects of polymer length and various molar fractions of the popular dimethoxyethane (DME) and dioxolane (DOL) solvents on the structure of the PTBT polymer at a temperature of 300 K. We characterize basic polymeric properties as well as the composition-dependent solvent adsorption structure and thermodynamics. Importantly, we find an interesting co-solvency effect, namely that a solvent comprised of about 25% DME and 75% DOL leads to maximum swelling (best solvent quality) behavior, which should be important for optimizing cathode fractality and permeability in applications. Our study thus reveals intriguing polymer-solvent correlations and serves as a first step for further MD studies of realistic polymeric cathode structures and processes, e.g., toward charge transport in vulcanized (S-linked) network topologies.