Using your browser's private or incognito mode prevents Bing from remembering your search history, but it's easy enough to manually clear your search engine's history even after browsing in its normal mode. You can do that from the site's Options page.
Open Bing in your browser and then open the search engine's settings by clicking the gear icon in the upper-right corner of the Bing page.
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Switch to the History tab and click Turn off to stop Bing from saving your future searches.
You can erase individual search results or all of them at once.
To erase a single result, place the mouse pointer over an item in the history and click Clear when it appears. If you don't see the item you want to erase, search for it using the search box on the page or click All dates to narrow the date range.
To erase all searches from your history, click Clear all. Then choose Yes, clear all search history to confirm you want to erase your entire history.
Optional: If you want to hide the automatic suggestions that pop up alongside your search history, go to Options and click the Settings tab. Then clear the checkbox for Turn suggestions on and click Save. If you like the suggestions, you don't need to turn them off in order to delete your history.
Clearing your Bing search history won't erase the history on your computer of searches performed through your Web browser's search bar. The method to delete these varies by browser. In Firefox, click the browser's settings button and choose History, then "Clear Recent History," and choose the time frame to delete. In Internet Explorer 10 or 11, click the "X" on a search history item in the address bar to erase it. To clear your entire history, open the Tools menu with the gear icon, choose "Safety" and click "Delete Browsing History." Check "History" and click "Delete" to erase both your browsing and search history. Chrome saves search history in tandem with browsing history. To erase a search, press "Ctrl-H" to open the history, check the box by the search result page for the search you want to delete and click "Remove Selected Items." To clear history in bulk, click "Clear Browsing Data" on the history page, check "Browsing History," choose a time frame, and click "Clear Browsing Data."
If you sign into Bing using your Microsoft account, the site saves your preferences and search history and makes it available on every computer that uses your account. If you don't sign into a Microsoft account, each computer has its own Bing search history using browser cookies.