Impossible to estimate the number of user using bitcoins because there are a lot of transactions going on and we cannot count how many transactions a person make on average like I do 10 transactions a day while a friend of mine gamble whole day and hence make 1000 tx per day.
This parameter would certainly not be the best for such analysis. Even using the number of wallets in existence is difficult to make a good estimate, because there are individuals who create different wallets. This is a study that should involve other analytical techniques, it could even include questionnaires to know which users are active on the network, and then make an estimate.