bing seems to remember everything I search

Depends whether you were signed in. Signed in: open your Microsoft account's privacy dashboard, Search history, Clear all, and on the same page switch off saving. Not signed in: those suggestions are coming from the browser rather than Bing, so clear browsing data in Edge or Chrome and tick browsing history and autofill. Bing also has its own search history page in the account menu with a clear button and an off switch. On a shared computer the honest fix is a private window for anything you'd rather not see pop up later.