I would try and hang it from a line or something in the middle of the book and see if it will dry that way.  or maybe try drying it with a blow dryer on a low setting?

I got a book in the mail before that was a soaked wet paperback. I sat the book up on the side and opened the pages so it could get air and then let it sit like that for a few days. If you have forced air heat you might want to put it close to that, also you might want to keep an eye on the pages so when some of them are kind of dry you can focus on some that are still wetter.

Good luck. :)

Likely the best method, and the one archives use, is freeze drying.  If you have a frost free freezer and you put the book in the freezer for about a week it should be dried with the minimum amount of damage.  Here's some information on freeze drying:  http://orpheus.ucsd.edu/preservation/howdry.html  (If it is not a frost free freezer it will not work.)

Is this an appropriate place to remind people that it never hurts to protect books in some kind of plastic before sending them out through the mail?

I think it's an appropriate place for sure.  Please protect your PBS books by using plastic (clean) of some sort before using the PBS wrapper.  It saves many books from many hazards including rain, and damp.  It's saved a book or 2 for me from the ravages of the USPS equipment.

Ruth

A very good place for a plastic reminder!  I got one today that was only wrapped in very torn brown paper and not much tape.  Luckily it's Saturday and I was home to intercept the carrier, otherwise I would have  come home to a wet mess of a book.

This is probably late advice, given the time you initially posted and how long it took me to see this, but I've had the best luck with placing sheets of cardstock cut down to page size, and inserted between every 3-5 pages or so throughout the book, placing it under weights (a couple of bricks), and then sitting it in front of a fan - open pages facing away from the fan - or near a heating vent.  Freezing in a frost free freezer is good because it helps remove the moisture, but you should still use the cardstock or even sheets of copier or printer paper between pages and keep it under weights until it's dry.  Otherwise, it's still likely to be badly rippled and the pages will be stiff.  No guarantees that it won't be anyway,  but I've dried out a few books this way, and it worked well on all of them.  At least one of them shows no signs of ever having been wet.

I have also ironed damp pages, which helps to dry them quicker as well as preventing those nasty ripples in the paper. Make sure the iron is not on "Steam"!

You could even set it up in front of a dehumifier if you have one. I set up one of those when my CARPET was soaked due to my washing machine backing up into the house, and even the carpet got dry eventually. How very disappointing, though. Good luck!