Hi MissThumann,
Wouldn't it be nice if they could just tell us what we all need to do to rank well? #wishfulthinking
As you probably know the ranking factors are not appreciably different for Bing/Yahoo than for Google, but you will always see some disparity between them. Based on this, I suggest that you make sure you are as diligent with your Bing Business Listing as you are with Google. We tend to put a major focus on Google, but ensuring that your Bing Business Listing is verified and filled out completely is an important starting point. That will assist you in locally ranking for Bing queries. Otherwise, look at those ranking ahead of you and see what they are doing you are not, then see if you can manipulate a page to rise in the rankings.
If you aren't try using Bing Webmaster Tools so you can find better insights into which pages are getting traffic through Bing and which aren't so you can determine which pages might need the content tweaked for Bing.
Like Julie suggested, find out how important it really is for this website to be ranking on Bing (or Yahoo). Do these search engines bring in enough traffic for you to devote a lot of time trying to decode the algorithm? Or are you better off putting most of your eggs in one basket with Google?
Good luck!