The most notable addition to the new interface is is smooth page transitions -- the fade in and out -- and navigation tabs (maps, images, videos, etc.) now persistently float at the top of the page. WinRumors is also reporting that a feature reminiscent of Google Instant search is being added to Bing, with page elements smoothly transitioning in and out as you type in your search query.
If you want to try out the new Bing UI, your best bet is to set your locale to United States - English and pray that you're part of the initial roll out. Alternatively, just wait a few days until MIX 2011, Microsoft's Web developer conference, which is when the new Bing UI should be officially launched.