A professor has offered to send me a hard copy of his new book. Would it be rude to ask for a PDF file instead?
It is a question of framing. Frame it as something that is good for him, not just for you. I'd write something along the lines of: 


  Thank you very much for your kind offer. I'm indeed  very interested in the subject of book X. It probably is easier and cheaper for you if you just send me a PDF, and as I am someone who reads mostly on a screen anyway, I would be equally happy with an electronic version.


(And then you might or might not mention your postal address anyway, but in any case stress again that it is up to him to decide.)

In fact, I have had such situations before (people asking me for a copy of my dissertation [which I would have send them for free in print], but who also mailed that they preferred a PDF).