Rudolph&Schmidt just released their second volume [Differential Geometry and Mathematical Physics II: Fiber bundles, Topology and Gauge fields][1], and it covers exactly this stuff.

These two volumes instantly became my favorite intro to geometric methods in theoretical physics. I'm sure in a few years they'll replace the likes of Nakahara due to their incredible mathematical completeness and physical insight.


  [1]: https://link.springer.com/book/10.1007/978-94-024-0959-8