Try using 'broken' link building.

There's several guides and posts here on Seomoz.  Just search.

Basically, you scan through the list of links, and you'll probably find a few broken or 404 pages.  Point those out and also recommend the addition of new resources, including your own.  It works extremely well, and you don't come across as the typical emailer that the webmaster probably encounters everyday.

Round off that strategy with a regular guest posts, link bait and other content marketing ...and you're solid.

Well bing doesn't crawl and index as much as google ...maybe they're even blocking Bingbot.  It's not unheard of.

Some blackhats/greyhats make it a point to block Mozbot, Majestic and other crawlers from their private networks.   That prevents links from appearing in competitive reports.

So try using Bing's Link Explorer given that they usually allow Bingbot and Googlebot to crawl.