High-resolution visuotactile sensors provide detailed contact information that is promising to infer the physical properties of objects in contact. This paper introduces a novel technique for high-resolution stiffness estimation of heterogeneous deformable objects using the Punyo bubble sensor. We developed an observation model for dense contact forces to estimate object stiffness using a visuotactile sensor and a dense force estimator. Additionally, we propose a neural volumetric stiffness field (VSF) formulation that represents stiffness as a continuous function, which allows dynamic point sampling at visuotactile sensor observation resolution. The neural VSF significantly reduces artifacts commonly associated with traditional point-based methods, particularly in stiff inclusion estimation and heterogeneous stiffness estimation. We further apply our method in a blind localization task, where objects within opaque bags are accurately modeled and localized, demonstrating the superior performance of neural VSF compared to existing techniques.