I covered this at Search Engine Land where I said early tests show that when on SSL search, the referrer query data does not pass through to your analytics. This means that the [not provided] count across search keywords will continue to rise.
But when I asked Microsoft about this, they promised that during their testing and roll out, they "will keep the SEO/SEM community needs top of mind."
Currently, this is an experiment, Microsoft told us:
At Bing we are always experimenting to improve the overall search experience and understand that people want choices in how they protect their privacy online. By providing optional access to Bing.com via HTTPS, we are giving everyone the ability to decide how they use Bing while also being thoughtful about how we implement this functionality.
But as they roll it out they will balance privacy and security with marketers interest.
Hope I had a more solid answer for you at this time but this is all I got.
Forum discussion at Hacker News.