Transporting Queen size mattress and box spring on car

Hello!

I'm moving in a few weeks and I have enough natural trips to my new hom/help with friends that I don't need to rent a moving truck. The only item that I'm worried about transporting is my queen sized mattress and boxspring.

I drive a Honda CR-V with no installed roof rack, although I do own one that attaches to the top of the door frame and is secured when I shut the doors on the hooks. I'm not super confident in it's ability to stay put though, and it also adds 6-8 inches to the top of the car which could get excessive if I were to pile a mattress and boxspring on top.

How do I go about moving this safely? I've got a ~110 mile trip from home to the Twin Cities and would likely be driving on 55 mph, 2 lane highways most of the way. I could zig-zag my way through country roads, but that's less ideal. Thanks for any help you can provide.