Dual-frequency RF systems are widely deployed in high-brightness synchrotron radiation light sources to achieve electron bunch lengthening. However, the transient beam loading effect induced by bunch gaps causes significant synchronous phase shifts, and severely compromises bunch-lengthening performance. To address this, we propose an active compensation scheme that suppresses voltage fluctuations in both the main and harmonic cavities by modulating only the driving voltage of the main cavity via a feedforward approach. To elucidate the underlying physical mechanisms, we establish a Gap-Induced Linear Decomposition analytical model, which decomposes the TBL-induced beam voltage into steady-state and transient components. Based on this model, we derive an optimization method to minimize power requirements, enabling the main cavity TBL compensation to achieve performance levels comparable to those of broadband cavity TBL compensation. The efficacy of this framework is demonstrated through two case studies: for an SSMB storage ring with a 7.5 MHz hardware half-bandwidth, the required single-cavity peak power is maintained at 158 kW, with normalized average radiation power improved from 78% to 97%; for the KEK-LS storage ring with a 6 MHz bandwidth, the single-cavity peak power is optimized to 148 kW, successfully restoring the average bunch length from 31.1 ps to 40.9 ps. The proposed scheme establishes a highly efficient and cost-effective paradigm for TBL suppression, providing a promising technical pathway for next-generation light sources.