Donor-bridge-acceptor (DBA) systems occupy a rich history in molecular electronics and photonics. A key property of DBA materials is their typically large and tunable (hyper)polarizabilities. While traditionally, classical descriptions such as the Clausius-Mossotti formalism have been used to relate molecular polarizabilities to bulk dielectric response, recent work has shown that these classical equations are inadequate for numerous materials classes. Creating high-dielectric organic materials is critically important for utilizing unconventional semiconductors in electronic circuitry. Employing a plane-wave density functional theory formalism, we investigate the dielectric response of highly polarizable DBA molecule-based thin films. Such films are found to have large dielectric response arising from cooperative effects between donor and acceptor units when mediated by a conjugated bridge. Moreover, the dielectric response can be systematically tuned by altering the building block donor, acceptor, or bridge structures and is found to be nonlinearly dependent on electric field strength. The computed dielectric constants are largely independent of the density functional employed, and qualitative trends are readily evident. Remarkably large computed dielectric constants >15.0 and capacitances >6.0 mu F/cm(2) are achieved for squaraine monolayers, significantly higher than in traditional organic dielectrics. Such calculations should provide a guide for designing high-capacitance organic dielectrics that should greatly enhance transistor performance.