It would be very difficult to define a meaningful general average, especially without more clearly defined parameters. As @Mark-C-Wallace has explained, the sizes of individual balneum varied widely. Their popularity and availability would have depended on where (the city of Rome itself, or the wider empire) and when (Roman bath culture spanned centuries) you are referring to.
Here are some helpful numbers to give some perspective though:
How popular the bathhouses were we could conclude from the fact that in 33 BC, there were 170 of them (public and private) in Rome alone. By the end of the 4th century AD, there were 11 public (some of them with a capacity of 2, 000 - 3, 000 bathers per day!) and 926 private baths in the Eternal City.
The largest complex of all was the Baths of Diocletian. According to this page, 3,000 was the upper range of it's daily visitor load. But this seems to be a conservative estimate and may have actually been what it accommodated at one time. The second largest complex was the Baths of Caracalla, and according to Wikipedia it could accomodate 6,000 to 8,000 bathers daily.
Based on these few data points, we might say that if we were only counting the major public balneum and ignoring the far more numerous privately-owned ones, daily average visitors peaked at least in the hundreds if not the thousands. A more inclusive average would have to be far lower.