I have lecture notes on my website that you might find helpful. They're from a one-semester graduate course (the second such course I've taught). Sadly, they're not yet typed...

They're a mix of material from Milnor and Stasheff, Hatcher's notes, and Husemoller's book Fibre Bundles. They cover vector bundles and principle bundles, characteristic classes and the Chern Character, and complex Bott periodicity. They don't cover representation rings or real K-theory. (I assume that in mentioning representation rings, you're talking about the Atiyah-Segal Theorem, or at least Atiyah's version for finite groups? I don't know any textbook reference for that.)

The proof of Bott periodicity that I give in the notes is a mixture of Hatcher's proof with some observations from Husemoller's book, and it uses the Chern Character to prove that the Bott map is injective. This is nice, because the proof of injectivity in Hatcher's notes (or Atiyah's book) is a bit more complicated that the proof of surjectivity. So if you're covering the Chern character anyway, this is a nice route to take.