I think the best way to see and experience the Loess Hills is not by any kind of motor vehicle, but by bicycle.
Once a year there is an event in August that does just that. It is called ONABIKE. Here is my blog post about it with pictures of the beautiful Loess Hills: History and Culture Part 206: ONABIKE
Head north of Dubuque and take great river road from there, great winding roads that follow the bluffs of the mississippi, stop at breitbachs country dining for a good bite (made it on national tv forget what station)