RockinChair, here are a few links to illustrated examples of exercises that I believe target and strengthen the muscles used to draw, steady, and shoot a bow. Note that you may perform any of the following exercises with either barbells, a bar, or cables. Dumbells and bars will add mass along with strength. Cables willadd strength with less mass.

Front Raises: http://www.exrx.net/WeightExercises/DeltoidAnterior/CBFrontRaise.html
Front Raises: http://www.exrx.net/WeightExercises/DeltoidAnterior/DBFrontRaise.html- These front raises will help with stabilizing the bow

Lying row: http://www.exrx.net/WeightExercises/DeltoidPosterior/DBLyingRearDeltRow.html
Seated One-Arm Row: http://www.exrx.net/WeightExercises/DeltoidPosterior/CBOneArmRearDeltRow.html- Exercises that involve a rowing motion will help you with the draw

Arnold Press: http://www.exrx.net/WeightExercises/DeltoidAnterior/DBArnoldPress.html- This is a good exercise to strengthen those muscles on the top of the shoulder and around your lateral andanterior deltiods. This will add strength and stability to your sholders. This will also make them look good

In addition to shoulder exercises, I would also suggest you add some back exercises to your routine. See a list at this link: http://www.exrx.net/Lists/ExList/BackWt.html. I also like dips. They are great for addressing the outer pectoral muscles as well as the shoulders and upper/middle back. You will get the best results from them if you do them in high reps, so you may like assisted dips during your buildup period. See an example here: http://www.exrx.net/WeightExercises/PectoralSternal/AsChestDip.html.As far as the back goes, I would focus on those exercises that target the upper and mid back, but don't ignore the lower back as it will assist you in keeping proper form. I

Holler if you have more questions. Good luck with your transition.