There are a couple of different kinds of e-readers you can get.  Some have screens that are not backlit, so they don't strain your eyes at all -- plus you can change the size of the text, making eye strain even less likely than when you're reading a book.  (Some books have such small print!)  Other e-readers have screens just like an iPhone, but I've never gotten any eye strain from those either.  I think part of it is that I am accustomed to looking at the computer for long periods of time, but part of it is also that I tend to turn down the brightness of the screen to only what I need in order to read comfortably.  I do the same with my computer, and I suspect that much of the eye strain people report actually could be resolved if they didn't keep their screens so bright.

Reading in bed is actually easier -- the e-reader is much lighter and easier to hold than many hardcover books these days (and some paperbacks too!).  And reading in the bathtub is resolved by putting my Nook in a gallon-size ziplock bag.  You have to make sure the bag is zipped up tight and doesn't have any holes (just in case you drop it in the water -- it'll give you at least a few seconds to rescue it, if not longer), but you can work all of the controls, even the touch screen, through the bag.

As for pricing -- this is a stickier subject for many people.  Prices for ebooks are lower than the prices for the hardcovers, but publishers have found that many people are willing to pay for ebooks, so newer books often cost just as much (if not more) for the ebook as they do for the paperback.  You can, however, get some good deals on older books in ebook format, and some publishers have periodic promotions where they give the first book in a series away for free or at a discounted price, or perhaps do the same with one of the author's older books when they have a new one coming out.  Also, many libraries now have growing ebook collections.

Sorry for the uber-long response, but I hope this has answered your questions!