There are places in this world where one drives on the left side of the road- mostly those with a connection to the British empire - and places where one drives on the right side of the road. Relatively few of these places are directly connected to one another and even fewer have a large amounts of traffic that would want to regularly travel back and forth (yes, I haven't forgotten the Chunnel).
However, Hong Kong and mainland China are such a place which has the problem. A Dutch architecture firm, NL Architects, has produced some visualizations of an elegant solution. They call it the "flipper bridge."
Image courtesy of Fast Company
This bridge was part of a entry in a competition connecting Hong Kong, Macau, and Zhuhai. Therefore, it is only fair to note this bridge was not part of the selected entry. And since this is a very uncommon problem, it is a solution we may never see put into place.