A fundamental objective of philosophy of science is to determine how scientific theories relate to reality. While much attention has been given to the ontological status of concepts like the wave function in quantum mechanics, the status of fiber bundles has received comparatively little discussion. This is unfortunate, given that our most fundamental physical theories can be written in the geometrical language of fiber bundles. More precisely, our currently most successful and fundamental physical theories—namely, the Standard Model of particle physics and general relativity—are gauge theories, and their most general mathematical framework is expressed in terms of fiber bundles. This naturally raises the question of whether fiber bundles are physically real. Although this question is not often explicitly addressed, it has been argued that similarly to how Einstein’s notorious hole argument rules out spacetime substantivalism, a generalized version of the argument rules out fiber bundle substantivalism. In my talk, I will show that by employing the recently established dressing field method, which eliminates gauge redundancy, we can construct a dressed principal bundle that is immune to the hole argument under certain conditions. This sheds new light on fiber bundle substantivalism and deepens our understanding of gauge theories.