In regards to your question, improving your ranking in Bing is very similar to the method that is used to improve your ranking well in to Google. One of the factors for improving your search ranking on Bing is through link building. The more 'quality links" that point to your site, the more likely it is that you will rank high for your target keywords. Other factors revolve around optimizing your title and description mega tags and writing compelling keyword rich content.
So what are all the main important things that Bing look for? Here below is a helpful link from a reputable site that provides a useful cheat sheet on what you can do to optimize your site for Bing.
Keep in mind the article is about 2 years old but will provide a "skeleton" of what Bing looks for.