adb, just shooting bows is one way that will indeed help you pull back heavier bows as your progress though your archery ..umm..career...for want of a better term. however, in the case of warbow archery, pulling a bow like a warbow is a different compound movement from target archery. compound strength is the net strength of all moving parts, so it will also help if you use bungee ropes to develop other muscles that contribute to the bow drawing movement (specifically bungee because unlike weights, bungee chords more accurately replicate the power curve of a bow which we would see if looking at a graph). that being said, it is important individually develop the forearms, elbow flexors, biceps, triceps, back muscles, rotator cuff, trunk, and even your butt. all those muscles work to pull the bow but there are many as well that need to "hold things in place" and stabilize the ones that carry the most load. constantly shooting is one way to do it, but if we dont use low poundage bows, some areas will not be worked and larger muscles take over, prevent those weak muscles from developing. im pretty certain thats why when the op switched to a lower poundage bow he felt a better pump where there was no pump before.
the ancients would have been working hard anyway, therefore working those smaller muscles in a number of ways, if (from what little i know) there was indeed a movement of yeomen who were trained as archers and employed by the government, there would have been some element of hard work that helped them develop the strength to use those legendary bows. they probably didnt have the same labour reducing technology that we have (whoohoo john deere tractors!)
mike made a good point, you need to sort of train everywhere to get stronger and prevent injury.
btw adb, is that the arms of the canadian warbow society on your shirt?