Would like some info on this as well. All I can give as input is that I've always just roughly assumed that the Bing search volume is ~10% of that of google on average. Also I've read that the average bing user is a 50+ year old male male making 100000k/year and in all honesty it does check out in my sites (my websites about tech gadgets that rank in bing don't get all that many visitors from there, my sites that target exactly 50+ year old men tend to do REALLY well). So my assumption would be that "iPhone cases" would get less than 10% of google search volume in bing, but "bladder problem remedies" would get about 20-ish percent. Those are sample keywords but you get the idea ... However this is all me playing a guessing game. I'd love if someone can share something I've missed in my work
I've been looking for this too. Like gazmo mentioned, you'd have to assume that ballpark figures of keywords searches would be relatively similar to Google. But it would definitely help to be able to see some solid numbers. I'm guessing they either don't want people to know those numbers, or they don't see a point since Google's search data would most likely give you the answers you're looking for only with inflated numbers for the larger audience.
Today someone ask the same question and he had a lot of nice answers. I remember that once answer was been something like. You can't get the good results by using just one tool. Use two tools and filter the results
http://www.bing.com/toolbox/keywords their official alternative to adwords keyword tool there is other one inside bing ads account but not good, at least from my point of view
I use the keyword discovery tool in Bing Ads to find the monthly searches for keywords on the Bing-Yahoo Network.
I don't I can necessarily "link" to it without it redirecting to a Bing login page. If you want to use the tool, log into your Bing Ads account, go to the campaign level, click on the "keywords" tab, go to "add keywords", and then click on the "Research Keywords" tab.
I never really focus on Bing to hard. Use GKP and focus on Google first. Normally Bing rankings will come along with it. Really you go after the best search engine first and let everything else follow.