Hello, It might be your website not index in bing...submit your website to http://bing.com/webmaster and wait for indexing
Just make sure that you understand how Bing selects it's website for indexing, read up as much as you can on it and you'll be able to get into bings top 10 ratings in no time flat
I've seen some similar results in terms of sites not ranking as well in Bing as they do in Google. At the end of the day, across the board, Google will supply far more traffic to your site for equivalent keywords, than Bing or Yahoo will. So don't worry, just focus on Google
Not only you have this problem. I have more than 10 keyword listed at google first page but never get indexed by Bing