In your scenario, you want to use Bing map in Power BI to relate Zip Code to lattitude/longitude. Right?
You should know that the Bing map in Power BI is just a visual. It can display maps based on lattitude, longitude or locations. However it cann't relate Zip Code to lattitude/longitude. So I'm afraid your requirement cannot be achieved in Power BI.
And I think you can try other ways. Please refer to following articles: