HV bushings are an important part of the equipment of large power transformers, responsible for their many serious (including catastrophic) failures. Their proper exploitation needs to apply correct and reliable diagnostics, e.g., the use of dielectric response methods, that take into account their specific construction and working conditions. In this article, based on laboratory tests carried out on a real bushing, it has been shown that the significant temperature distribution within its core significantly affects the shape of the dielectric response of its insulation; therefore, the approach to its modeling should be changed. Hence, a new method for interpreting the results, using the so-called the 2XY model, is proposed. Subsequently, based on the measurements made on the insulators in operation, a new modeling method was verified. In conclusion, it can be stated that the 2XY model significantly improves the reliability of the dielectric response analysis, which should be confirmed in the future by tests on withdrawn and revised insulators.