Yahoo no longer has a search engine. Since 2010, its search results have been powered by Bing – which means that they are Bing's search results.
Google has the highest market share for all search engines and you can see the recent figures on my Hub at this section:
Google and Bing use different algorithms to determine search results. Google has spent more money investing in its search quality and its search engine is the most used and most trusted. Since you are ranking well on Google, I wouldn't worry about Bing.