This is why science is cool. 
>It takes time for the electrons in the glass to pick up speed and start oscillating in time with the sine waves in the white light. This is what causes the dispersion.
I think this is wrong. I’m sure the time delay, or reluctance to comply instantly, causes a phase shift between the electrons and the wave that is exciting them. It doesn’t make them resonate gently at first and gradually more vigorously over a number of cycles. Offhand I’m not too sure, but am guessing that the phase shift being a mild function of the frequency is all it takes to have dispersion.
There’s also a response time issue for electrons in a metal, that influences how quickly the metal can conduct. I read in a book about electrical resistance (yes, the entire book is about the resistance of metal conductors to current flow) about this. I think this is the reason for one kind of skin effect, though I think maybe there’s something else relating to inductance and the whole topic is a bit unclear. In any case, the response time issue in conductors is an obscure and unimportant and tiny effect in the case of many resistors and other circuit components, I gathered.