Why is Bing seen as the only other game in town? If you're really about not letting 'the man' in on your stuff, why would you go to the other 'the man' of Microsoft?
I don't use them, but my privacy-conscious friends use duckduckgo for this exact reason, and it has a wealth of rich search available.
Also, something in me philosophically opposes a mail company that charges 50% more for IMAP access. IMAP should be encouraged for the masses, not shunted into a 'you-only-want-it-if-you-know-it' space. IMAP solves most of the problems I hear from normal users that isn't password-related.