This isn't exactly to my satisfaction on scientificalness of approach, but the best numbers I was able to find so far come out of this:
Match.com, which helped to pioneer the online dating industry, has revealed the results of its Singles in America: 2013 survey. More than 5,000 single men and women 18 and older participated in the survey. Here are some of the findings:
92% of single men feel comfortable if/when a woman asks them out
The "big three" criteria by which singles judge a date are grammar (83%), confidence (78%) and teeth (76%)
Elsewhere in that survey, it was mentioned that 83% of men wanted a confident woman, which means that the above generic 78% (assuming 50/50 survey response breakdown) would imply ~73% of women prefer confident men.
Obviously, this suffers from faults (self selection bias, demographics bias, bias of people pressured to respond to make a favourable opinion of themselves, as well as some assumptions outlined above). But it's the best I could find, and seems to indicate that confidence in a man is a pretty important factor as stated by Match.com responders.
Another possible fault of this survey (but it would be inherent in almost all sources using what people say vs. what they do) is that there may very well be a large discrepancy between revealed and stated preferences, that would be impossible to detect absent actual behavioral observation. (And even a behavioral observation would not necessarily be accurate unless done "in the wild", so to speak - without the pressure of being observed and judged by researchers).
There's no raw data available for the survey, but all the figures quoted above are found on their infographics/websites: http://blog.match.com/category/singles-in-america/ and http://www.singlesinamerica.com/