I've never been happy with how Bing handles geo-location detection of web sites. They use and rely mostly on the meta language tag to determine if the site should be in Bing US versus a localized version of Bing. Google's Matt Cutts somewhat mocked how Bing handles this by saying:
Historically, meta tags for language and country have been less reliable than inferring the language or country directly. For example, lots of webmaster also just copy/paste from a friend's template without checking the meta tag values. The unreliability of the meta tags is why Google tends not to use them or give them less weight.
That being said, this is how Bing handles it and if you see your site in a regional Bing that doesn't make sense, you can change it by updating your meta language tag.
Brett Yount said in a Bing Community thread that once this is updated, Bing should update your site within one or two crawls. Brett said:
Change that and the issue should be corrected within one or two crawls.
So overall, if your site gets crawled once per day, you should be fine within a couple days.
Forum discussion at Bing Community.