Christi Olson from Bing has said that they "have no plans to do a Bing 'mobile first' index."
Jennifer Slegg at The SEM Post makes an interesting point - since Bing isn't going mobile, this makes it a lot more difficult to optimize for both search engines. "For those sites that consider Bing an important traffic source [they] will now have to optimize the mobile version of a page for Google,w hile having to optimize the desktop version for Bing." Responsive sites probably get away cheap from this, but sites with separate mobile versions could have a headache on their shoulders. And what about Yahoo, which switches back and forth between Google and Bing?