I think the general consensus is that if you're optimized for Google, you should do fine in the others. See this previous Question
Although the discussions there are from 2010, I think most of it still holds true.
A few differences between Google and Bing are:
- Bing looks for keywords to match the content exactly, whereas Google will allow for synonyms and more contextual meanings. So you might want to examine how your keywords appear in your content.
- Google pays less attention to domain age than Bing, which places more importance on this. So if your domain is new, it may rank lower in Bing than Google.
- Bing may prioritize local results first, particularly for ambiguous search requests. So if your site is not locally based, then it may rank higher in Google.
- Google is fine with forums, but Bing isn't, so if your site is heavily centered around a forum(s), that might be one issue causing a lower ranking in Bing.