If you need something that feels more safe than a ziploc baggie, then have a look at the m-edge guardian case. It is made for the kindle 2, but I use mine with my Sony 505, with some strips of foam core to keep the reader from rattling around in the case. So I figure it ought to work for the 350 as well?
The case is on sale:
http://www.medgestore.com/products/kindle2-guardian.psp
Of course you need to check if you can access the buttons for page turn, I'm not familiar with the layout of the 350