This study serves as a natural continuation of the work initiated by Afzal et al. (2025) [4], where the authors established boundedness results for the exponentially damped Riesz potential within the setting of variable exponent Lebesgue spaces. Through non-trivial examples, they demonstrated that this operator possesses richer structural properties compared to the classical Riesz potential. In the present work, we extend this investigation by introducing a new class of exponentially damped Bessel–Riesz potentials. As a first step, we establish the boundedness of these operators under a variety of appropriate assumptions. Unlike the previous study, which relied on Lebesgue spaces, we work within the framework of Herz spaces, which offer a more refined structure for capturing both local and global behaviors. To demonstrate the practical significance of our theoretical findings, we apply the main boundedness results to analyze the regularity of solutions to a nonlinear parabolic Black–Scholes-type equation. In particular, we employ our operator estimates to control the standard linearization expansion associated with the parabolic system. The proof strategy is based on decomposing summation terms and deriving sharp estimates under various structural conditions. Finally, to highlight the generality and strength of our approach, we show that several known results emerge as special cases of our framework.