There were episodes where Jesse reminisced on her school days, meaning she has already gone through that. Plus the special team rocket training, and the time between that and meeting ash (and James before that) she has to be 20 something. Therefore, James should be as well.
-Kass
Source: look up James on bulbapedia since apparently I can't post any goddamn links
Bio section, right before contest disguises.
Supposed to be same age as Ash in GAMES. Is over 20 in anime.