In saying that it's not a truss rod adjustment but a bridge adjustment, I'm guessing you are saying that the high action is most noticeable toward the end of the fretboard between the 12th and 24th frets. If the action is as high in the middle of the fretboard, around the 7th and 9th frets, then that would suggest a truss rod adjustment.
But assuming it's a bridge adjustment. Are you playing heavy gauge strings? If so, it could be that the strings are riding high in the saddle slots. What you can do is widen the saddle slots so that the strings rest lower in the slots. If the strings are not too wide for the slots, then what you can do is deepen the slots. You can do this with a needle file, and some very fine sandpaper to smooth the edges; and I've found that a magnifying glass is very helpful. You'll want to take your time and make sure that the relative slot heights are consistent.