The ideal transport is one in which you have to make a minimum of effort and certainly do not have to buy additional mounts. Such transport will serve as a large truck for crossings.
Can a car be used? Yes. But you need to remember that it’s worth transporting a mattress in the trunk only if the twisting method is suitable for your type of mattress, and the mattress itself is no more than a meter wide (otherwise it simply won’t fit, and you can’t fold it across).
Is it possible to transport a mattress on the roof of a car? Carrying a mattress on the roof of a car is a very difficult and risky idea, because if the dimensions of the mattress exceed the width of the car, you can get a fine. Also, the mattress can get loose and fly into the windshield of other road users, and it can also play the “sail” effect and the car will simply skid. If you decide to transport the mattress on the roof, use strong straps with secure latches, such as a tow rope or a ratchet tie down strap.