Granted, some of them have been hiding in the background for a long time -- the hasfeed: operator is one of my favorite hidden gems. [Here's how it works -- to look for a page that has an RSS feed and that has the word apiculture, use the query apiculture hasfeed: ]
Some of the other operators offer some interesting possibilities... Take the norelax: operator, for example. Bing's default with a search query of five or more words is to "relax" the requirement that the fifth and later words appear in each search result. Norelax:search_term tells Bing that this search term, even if in a string of four or more other words, must be in each search result.
Then there's instreamset:, which lets you combine fields in which you want to limit your search words. If you want to limit your search to words in the title or anchor, you can use instreamset:(title anchor):search_term You can include any combination of title, body, anchor and URL.
If you think Bing's only for casual use, check out these advanced search operators.