ehhhh....old perspiration stains are very tough to remove, if possible at all. i regularly get stuff at work i cant get out. 
if youre going to bleach, test an area first if the jersey isnt 100% cotton, some synthetics (such as polysester) can yellow when bleached...and you dont want the whole shirt to look like it got pissed on 
 
also, soaking it for a *long* time may help. odds are this isnt coming out, being so old, and having been washed and dried many times before. if a drycleaner is nearby ask if they can give it a try; its not unusual for us to work on a customers garment for specific stains before we clean things (indeed, stains are often removed better before a cleaning) but if its something very bad we dont charge them for it, since we couldnt do anything. Worth a shot anyway...but i imagine youll end up needing a new jersey, or wearing one with yellowed pits :/