I use Google Chrome, and have never had this issue. But here are some things you can do:
1. Download and run the excellent adware/malware program Malwarebytes, available from here:
https://www.malwarebytes.com/mac/
It will do a "decent" job of finding adware/malware.
2. If you still have Google Chrome installed, download the excellent free program AppCleaner, available from here:
https://freemacsoft.net/appcleaner/
It does an excellent job of finding most (maybe all?) files/folders, etc. associated with an app one wants to remove/delete (and of course the app itself).
For any left over "stuff", you can do a search of your drive. In your case, you could use "Bing" as the search term, and then Google Chrome. Spotlight is OK for such a task, but I prefer the excellent free program EasyFind, available from here:
https://www.devontechnologies.com/products/freeware.html
3. Make sure you are using the latest version of Google Chrome. And after you install it and select Preferences, you should see the setting for "Search Engine". Mine says "Google", but there is a "selector/down arrow" next to it, and when one clicks on the arrow, a choice of 5 Search Engines to choose from appears (two of them being Google and Bing).