I like Naber's books too (I would have liked them even more, if he had used the "definition environment" and less boldface... the pages look a bit too dense and heavy). Other books on the topic (with similar style):
Introductory books for mathematicians, but easy to read:
The book "Connections, Curvature, and Cohomology, Vol. 2" by Halperin, Greub, Vanstone is more advanced, useful for general reference; vector bundles, which are fibre bundles, are discussed in vol. 1.
Holomorphic vector bundles need some basic knowledge of sheaf theory and sheaf cohomology, they are interesting on their own but also useful for two-dimensional CFTs and Chern-Simon quantization (and geometric quantisation, in general). They are explained in Griffiths, Harris - Principles of Algebraic Geometry, Huybrechts - Complex geometry, Wells - Differential analysis on complex manifolds, for example.
The review by Viallet and Daniel https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.52.175 is a good place to start, if you're interested in gauge theories: it's really motivating.