Just for the heck of it I just grepped the log on my one server. It's got about 200 different domains, mostly smaller sites. About 600k hits today. ~5,000 referrals from Google, ~200 from Bing. Strangely enough there seems to be about 11,000 hits from Bingbot and only about half that from Googlebot crawlers.
I'd be interested in hearing how those numbers compare to other sites.
Google has indexed more than 50 times as many pages as Bing on that site, and crawls far more aggressively (over a million pages per day), which will both be factors, but the main one is probably still that Bing has less visitors.
So for me Bing is still irrelevant as a source of traffic. Even though I'd prefer to see some competition for Google, there just isn't any. DuckDuckGo referred me just 32 visitors yesterday, so they have even further to go!
Although my site is in English, over 50% of visitors are from outside the US. Bing doesn't really have the global reach of Google.
For example I get 250 times as much traffic from India with Google rather than Bing, 1000 times as much in Indonesia. Compared to 36 times as much in the US (which is much closer to the ratio of the other sites, which may be more US-focused).
It's probably a bit harsh to call Bing a "local US search engine" (like Baidu and Yandex in their countries), but it certainly needs to get more market share in other countries to compete globally.