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This will fix the issue on Bing for users, but Bing must have found this URL somehow, so presumably there is a link somewhere to the non www and the link is powerful enough to get bing confused, so another reason for the 301.
you should also consider a few other possible problems:
- make sure the indexed non-canonical url doesn't also have additional misspelling, missing or wrong punctuation, etc that could be causing the "not found" error.
- check that your custom "not found" page is returning a HTTP 404 response rather than a 200 OK.