It seems that the concensus is that the East headwaters where Rocky Creek meets Bridger Creek. I would like to argue otherwise, to ultimately open up a few more miles of this river in the winter (when the East remains open, but Rocky Creek is closed).
The BLM and USGS maps clearly mark it as the East Gallatin up to the confluence of Kelly Creek and Rocky Creek. Moreover, if you search Kelly Creek on Montana Fish WIldlife and Parks' website, it is listed as a tributary to the East Gallatin River. These two things give you enough of an argument to fish up to Kelly Creek year round, even if the residents of Rocky Creek Road (downstream of the confluence of Rocky and Kelly on the EAST GALLATIN) tell you otherwise.