Drawig a bow and shooting a bow are very unique dynamics that are hard to replicate in the gym. With that said their are a lot of movements that you can do to help improve strength, for the large back muscles you can do pull ups, dumbbell and barbell bent over rows, deadlifts, and the bench press. For the shoulders you can do military presses, farmer walks, sledge hammer work against a tire. But do not forget the smaller muscle groups around the shoulders and into the back, things like front and side laterals, reverse rowes, and a rowing machine, these will all help strengthen up the muscles.
You can also do bow specific drills, like holding the bow at the full draw position for 15 to 30 seconds and then resting for a minute, and then repeat this drill for as long as you can. The thing about this drill to remember is to try to transfer the weight into the large back muscles. If you are only using your shoulder muscles you are you going to run into problems real quick. You can also place a 5 to 10 pound stretch band over your bow so that you are drawing 5 to 10 pounds more than you typical weight. Make sure you do this only as a holding drill and do not try to shoot any arrows this way.
Another thing to keep in mind is rest and recovery, this is a critical step that most people overlook. Sometimes it does the muscles more good to take a days rest in between shooting and workout sessions so that they do have time to recover. Most of all do not overbow yourself, this will take away from your shooting form and you will get frustrated real quick.