I have a site that's about 2 years old. It gets tens of thousands of daily visits from Google, and usually less than 100 a day from Bing. I actually get more traffic from Ask.com.
Bing has hated the site from the day it was born. Looking back through my analytics, there was never a spike or a dip. It's just been predictably miserable since day 1 (this was a new domain at the time, never registered before).
I've never had this problem before with any site. Usually, Bing has been the easy one.
I realize this is a very hard question to answer, but have you seen anything in the past that impeded ranking well on Bing?
I have the same trouble and it's something I want to delve into. Is your site fully indexed by bing? Mine is about 1/4 indexed now but I haven't seen any significant increase in traffic from bing, as I come up pages deep in the SERP most of the time and my pages are newly indexed. I'm uncertain how fast newly indexed page reach the SERP.