If you're using Bing anyways, consider switching to Ecosia, it's a non-profit search engine, they pull their search results from Bing and plant trees across the globe with their profits.
It might not be for extremely privacy conscious people because they do send some of your data (obfuscated IP addresses, user agent string etc.) to Microsoft because they use Bing but it's still orders of magnitude better than using Bing directly.
Ecosia always sent user data to Microsoft (Bing), it's just that they will also be pulling search results from Google now so now they're contractually bound to send some data to Google as well.
The point is that it never was for extremely privacy minded folks, it's ofcourse a better choice than using Google or Bing directly because you're atleast not getting profiled as far as I can tell, but it can only do so much when it is dependent on ad revenue and has to work with Bing and Google for search results.
I'm not a privacy expert and this is just my opinion as a fellow Ecosia user, so take this with a grain of salt.