Most of the traffic at present is probably just from web publishers seeing what they rank for, compared to Google. As the TV ads kick in, more of the general public are bound to give it a shot.
The name allows people to 'verb' it, so you can say "Why don't you bing for your nearest pizzeria?" in the same way that you would talk about Googling for something.
Search results themselves appear to be sensible, no junk apparent as yet, and you have to wonder how the underlying technology differs from Google's.
One neat feature is the text preview that pops up on the right hand side as you mouse over the results. This gives you an idea of what else is on that page, and a handful of other links present on that page.
Go to Bing.com to give it a workout. For your information, Live.com (Microsoft's incumbent search engine) now redirects to Bing, so the software giant is really going for this one.