Just out of curiosity, I searched (not using Bing) for three terms: bing no results
There were thousands of hits, and each one I checked showed people asking the same as Basil. But there were never any real answers or suggestions, other than "try it again tomorrow" or "sometimes Bing defaults to only a local search".
It's like thousands of people over the last several years have experienced the same thing - but even from MS there are no answers.
Question: if you searched via Bing for "british car forum" (for example), and got "no results" - were there any ads for British car items, or "related searches" listed on the "no results" page?