What size cutting mat are you taking? I keep my cutting mats in one of these:
http://www.artistsupplysource.com/pr...roductid=31843
I have all of my cutting mats in this case. My flat mats and my two rotating cutting mats so it holds alot. It has two pockets. It keeps them nice and flat and protected. When I'm not using them it just slides under my couch (the one where there is no baseboard heating). I have the 18x24 size so my largest one does not go in the case but it stays on the cutting table anyway.
I am able to fit my rulers and cutter and a few other odds and ends in the same case. Even though it looks flat it holds a good deal of stuff. It has a well padded handle as well as a shoulder strap. One of the things that I like about this is that it is supportive and protective to the mats. I also like the shoulder strap. I found mine at Tuesday Morning for $11.99 but if you don't have Tuesday Morning or they don't have them they can also be purchased online or I would try an art supply store that might be local to you.
If you have a case like this you can feel comfortable putting it flat in the back of the vehicle and then putting things on top of it without any damage to your mat.