Submitting the url to webmaster alone is not important. Has to be more careful about the metatag. Make sure metatag for each page is given and if possible make it unique. Try to give maximum keywords and avoid repetition of same words.
There are several ways to improve your ranking with bing. One is to make use of social media on your website. Using backlinks is also a good way. This is useful if you have a blog or a forum. Keeping the content on your site fresh and interesting is important. This will also increase backlinks and social media activity, which can aid your ranking.
I think if you get good ranking result at Google then you will also get some help to increase your ranking on bing...
Write long and original content on your pages Domain age is really important. Page titles. God of SEO : Backlinks. Link out to important page
On-page - Good title , description, keyword density Off - page - A few keyword anchors from authority site would get you rank. Repeat off - page every 2 weeks if see progress.
I had researched a lot on this and have published an article on SMG Convonix blog. You can view it here - http://www.convonix.com/blog/beyond-google-how-to-optimize-a-site-for-search-on-bing/.
Seems like old SEO I guess. So people who are known with SEO can always do a good job in Bing search results.
Try implement and improve these things you'll have results: Improve your CTR Building High Quality Links Reduce your Bounce Rate Use Schema.org Use Bing’s Webmaster Center Produce Quality Content Work on your Internal Link Architecture Improve your Crawlability On-page Optimization Mind the user experience Select carefully your Domain name Use Social Media Buttons & be Social Active Don’t use Blackhat Methods Improve your Website Structure Mind the GEO signals