Okay, it was like impossible to find this link so I am posting it here publicly for future reference: https://www.microsoft.com/en-us/corporate-responsibility/content-removal-requests-report?activetab=pivot_1:primaryr7. Microsoft determines the right to remove content based on a users location. For example, they are bound by certain privacy laws in places such as Europe, or Russia. This allows content removal in these countries to be easier than it may be for the rest of us. From this page, you can request that information be removed from Bing.
If you are looking to remove content based on copyright infringement, you may do that here.
If you are looking to remove content from Google, go here: Remove from Google