Unfortunately I have been—and still am until I can afford a car—restricted to taking the bus for transportation. I have taken many trips, at many times, in many places, with many people. One thing I have noticed and been interested by is the judgment—or lack thereof—that people use in determining when to pull the stop-request cord.
Some people pull it immediately after leaving the stop prior to the one they want—some even earlier than that. Some people pull it exactly halfway, others wait until the bus has all but passed the stop—or even after—and the rest pull somewhere in between.
The ideal time to pull it is simply a case of common sense. You do not want to pull it too early because then the bus driver will slow down right away to avoid passing the stop, thus delaying your arrival. You do not want to pull it too late or the driver may not have enough time to stop and will just pass it and stop at the next one. There is no specific number or fraction that I can give since inter-stop distances vary as do road conditions and traffic, but ideally, you will want to pull the cord as close as possible to the stop while giving the driver enough time and space to safely come to a stop. A general rule of thumb could be to wait until you are about 2/3 of the way to your stop from the previous one.