My old 9" Fujitsu (a "netbook" from the days before they invented the word "netbook") has survived 100+ days of touring over 5 years simply wrapped in a homemade bubble-wrap envelope carried in my handlebar bag.
And really, I think the pouch is even mostly psychological comfort for me rather than any protection for the computer. It's just a flat piece of bubble-wrap taped together to make a form-fitting sleeve. The bubbles tend to flatten over the course of a tour, and though it maybe could add a little water resistance, but it's certainly not waterproof. My water-resistant handlebar bag w/ raincover takes care of that aspect. I like the easy accessibility where I can slide it out of the sleeve on the side of the road and have it up-and-running in seconds to check a turn or the location of the library.
You won't be able to fit a 10" eee into a handlebar bag though, so I agree with others, just throw it in with your clothes, maybe inside a Ziploc if you don't do a great job of keeping water out of your bags.
Neil