BusinessWeek gets its story from the usual "people familiar with the matter" (two of them, in fact). They claim the talks have been going on for weeks, but that a deal is still far off. Supposedly, this is all a consequence of the increasing rivalry between the once comfy-cosy Google and Apple.
Increasingly, Google and Apple are becoming each other's competitors. Google started the Android project which competes with the iPhone's operating system, and of course also launched the Nexus One, which competes directly with the iPhone. On top of that, Apple is getting into mobile advertising, and Google will be launching its own desktop operating system, too.
"Apple and Google know the other is their primary enemy," claims one of BusinessWeek people who is familiar with the matter, "Microsoft is now a pawn in that battle."
If the talks did conclude with a deal between Apple and Microsoft, Bing may become the default search engine on the iPhone, requiring users to actively change it to Google or Yahoo. As it stands today, Bing is not even an option on the iPhone - you need to either browse to its website, or download the (admittedly, nice) Bing iPhone application.
While the "Bing-as-a-default"-thing surely makes for better headlines, reality is probably that Microsoft wants Bing as an option on the iPhone (alongside Google and Yahoo) and/or on Safari for Mac OS X.
The familiar people even state that Apple is looking into creating a search offering of its own - which sounds even more outlandish to me. A search engine is not an MP3 player - it takes years and years of steady indexing to get it right, and it seems unlikely to me that Apple is indexing the web in a basement somewhere at Infinite Loop.