I think it would take a lot of research for that. There are factors that make it difficult, such as the fact that many users are anonymous. This can cause a significant margin of error. But if the research is done so that users could also participate anonymously, this problem could be mitigated.
Most probably not all bitcoin users would participate in that survey for the population of bitcoins and even a single troll can create a script that would spam the survey and enter random information just to, you know, mess up the whole statistics thing. Since we're all anonymous, anyone can do anything and I think that would always end up with no success at all most especially at a topic as insignificant as this - identifying how many bitcoin users there are. We don't even need that data that much.
It's indeed pointless to trust on surveys as they can be easily manipulated. But I personally don't even bother with trying to know how many people are using Bitcoin.
Mainly because of the fact that it is difficult to categorize people as Bitcoin user.
Do people need to use Bitcoin once a month, once a week, several times a week, or is once a year enough to mark someone as a Bitcoin user.
If you look at the transaction volumes, then it's safe to say that the level of usage has significantly increased over the years. But yet again it doesn't point to a number of people using Bitcoin.
