my questions
1,How to improve my ranking in bing
2,which way I check my backlinks on Bing search engine?
There are many ways. Try submitting your sitemap to Bing Webmaster. It works almost the same way as Google Webmaster.
Following the same technique which you optimize for Google. Only few difference is there. Bing give importance to No follow and reciprocal links in limited manners. For checking Backlinks, Use Bing Webmasters tool.
Submit to Bing Webmaster and do pretty the same you would do with Google.
There is no special backlink checker for Bing search engine. We can check as normal. To improve ranking on Bing we should follow the websites which are listed in Bing.
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.