This is what to do: Navigate to the Bing homepage. Click on the four horizontal lines in the top right-hand corner. Click 'search history' once in the drop-down menu. On the next page, click 'clear search history' on the right-hand side. Your browsing history should now be deleted and your cache clear!

Scroll down a bit to the "Search History" section, and then click "View And Clear Search History" button. This opens the "Activity History" tab of your dashboard, and puts the focus on your past searches. If what you want to do is clear your entire search history, you can just click the "Clear Activity" link at the top right of your search list.