We're moving a site, we've set up 301's from the old pages to the new ones and told Google about the move, but I couldn't find any were to tell Bing. Is there a feature to do this in Bing Webmaster Tools?
Here are instructions on how to tell Bing you have moved site: Bing Site Move tool
The Site Move tool, located under Diagnostics & Tools can be used to tell Bing that you have moved and permanently redirected your site (or a section of your site) to a new location. Although permanently redirecting your URLs using 301 redirects is sufficient for Bing to understand that you want the new URLs to be indexed instead of the old ones and this normally happens automatically, the Site Move tool can help expedite this process.