You have a few options. First off, what style frame does the bike have? If it has a traditional diamond shape frame, any style rack should work. If the top tube of the bike is sloped down, like a 'women's style' frame of old or a beach cruiser, it will not fit on a bike rack that has the arms coming off the top (ie- google Yakima Kingpin). A $30 adapter would be required to take the place of that top tube. (google Yakima Y02531).
The other alternative, though a little more expensive would be a rack that supports the bike by the wheels and uses a clamp against the frame or front tire to support the bike. Just about any bike should fit in those. (google Yakima Holdup).
I used Yakima as a base to search because they are available at most shops. You can find Kuat, Thule, and Yakima at most places. I don't know about shops local to you, but I work at a shop in the Charlotte area. Be prepared to spend $250 or more for a hitch rack. All should be light enough for her to use and attach/remove. The bike probably will weigh as much as the rack...
