Of course you can. You just need to make sure your hands are relatively dry, and that you don't drop it. These rules are identical to those for reading a traditional book in the bath, although I will concede that the stakes are higher due to the cost of replacing a Kindle compared to that of most books*. However, I'd be prepared to bet a couple of peanuts (and maybe even a brazil or two) that my Kindle could take a quick dunk as long as it was thoroughly dried and then left in a bag of rice soon afterwards (although I wouldn't want to try this on purpose), which wouldn't necessarily be the case with a standard paperback.
You can also buy special cases, such as the Aquapac, to make bathtime reading safer, and this is something you just can't do with a 'real' book unless you only get through one page per soaking session (in which case, again, you're doing it wrong). In fact, with my covered Kindle I can even read a book in the shower. Beat that, Luddites!
It just crossed my mind that you could probably manufacture your own cheaper but less reusable waterproof e-book cover with a sandwich bag and some duct tape. But don't quote me on that.
* Although it's not necessarily, as my friend experienced, as high as you might think.