The best is to shoot your bow year round. It's not all about pulling the bow either. That's the easy part. You have to train the brain as well because once you have the bow at full draw it's 90% a mental game.
Of course the gym doesn't hurt anything either. It takes more than arm, shoulder, and back muscles to be able to shoot effectively. It's just like putting up a building. You start with a sound foundation and for shooting that means starting from the bottom and working your way up.