Probably not fair to say that the fibre bundle perspective is ignore in physics, but whatever.
To the extent that you want rigorous math, the issue is of course open. As for using the theory to attain results via computation, the approach is - as with simpler QFT's - a path integral that you approach term by term via Feynman diagrams, some of which you can see here
https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory#QuantizationIf you come from a mathematical perspective with some background knowledge on Lie theory, maybe focus on the su valued forms A, or whatnot, on space.
There's mathematically pretty questions tied to that, e.g. gauge fixing to mod out the gauge space in an integral, where you don't want to double count contributions from one and the same physical configuration twice. I guess see e.g.
https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghostThere's also a more operator-theoretic perspective.
Peskin and Schröder is a book that will certainly discuss some, of maybe Rider for a start. I haven't caught up with QFT book in the last 8 years. But I don't think the "for mathematicans" books are very good.
(You probably wouldn't recomment "Measure theory for Engineers" or "Class field theory for Engineers" to an engineer either, those are generally brutalizations of a subject.)
