The new API documentation can be read over here and allows you to take everything you see in Bing Webmaster Tools out of it with the exception of messaging and the keyword research data.
To access your Bing Webmaster Tools API, login and on the left hand navigation, you will see the option to access the API. Click on it, agree to the terms and then generate an API Key to give to your developer.
This is a pretty exciting announcement from Bing, opening up their data to developers.
Of course, Google Webmaster Tools already had an API for a while.