I thought about a tarp, but I was concerned about the packablity of it. I have taken a 6x8 (I think that is the size that I have) tarp on short trips, but it took up a lot of room.

http://www.wiggle.com/bikeparka-the-urban-bike-cover/

I found the above in my searching last night, but $50 is pricey. Maybe just covering the saddle is the best idea? I need to thank about it more. Thank you for the suggestions. I am interested in more thoughts on the topic.

Blakcloud, I was very interested in your post as I was reading it, that is, until I got to the end of it. Do you remember the name of the one cover that you like?