Bing does not support listing suppression, meaning that any duplicate listings will not be removed. Although Bing does not support listing suppression, there is an alternative way to have duplicate listings downgraded and possibly removed.
To do this, navigate to the Bing listing that needs to be removed, and click to open the listing window. Next, click the three dots in the top right-hand corner, and select "Suggest an edit."
From here, you can select "remove this place" to have the listing marked as closed, nonexistent, or duplicate.
By doing this, the listing may be displayed less frequently, and the correct listing will likely come up first.
NOTE: The more people that do this, the faster the wrong entry in Bing will be downgraded.