It's plenty light enough to go in a backpack or messenger bag, as long as it has some kind of protective sleeve to keep the screen from getting scratched.
I haven't actually taken mine on the bike, but there's no reason you couldn't. You'd want to insulate it a little from the worst of the road vibration - make sure it's not contacting stays, etc. - but I really wouldn't worry about it. Time was, my laptops had thousands of miles on the motos with no problem, and with no moving parts, an ereader will be even less prone to vibration damage. The Sony comes with a neoprene sleeve which is plenty to insulate from scratches and vibration IMO. If you wanted a little more protection you could just wrap it in a towel or stick it in a bubble-wrap envelope.
One thing nobody's mentioned is the ability to re-size text. It's nice not to wear my reading glasses sometimes ... although after a certain font size, you start having to turn pages so often that that gets annoying, too.
Speed comes from what you put behind you. - Judi Ketteler