I have been a card-caring member of RSC for about a decade now. I can confirm the registration fee and that they probably have the most comprehensive Bianchi registry, at least that I know of.
As for your bike, if it is a corsa, the earliest on the registry is from 1915 and has the serial number of 4569. 5-digit numbers seem to start and end in the early to mid 1920s. 6-digit number/letter combinations started in 1925.
If your bike is a viaggio, the earliest on the registry is from 1902 and has the serial number of 7102. These go up to 81105 by 1909. Then the registry says Bianchi did a reset of their serial numbers. They have 13105 as a bike from 1911. This continues until 1914 which ends with 45340. Bianchi again reset their serial numbers in 1915 and have example 2572 on their list. By 1919 they have 96240. Another reset in 1919 and have an example from 1924 as 80458. And like the corsa bikes they go to 6 digits in 1925.
Based on numbers alone, which is never absolute, that would put your bike as either 1909, 1919 or 1924. But again, I have seen examples that don't fall in line with their serial system.
Do you have pictures of your Bianchi you can share?