Head over to Modells or any good sporting goods shop and get yourself one of these. Start out with the "light" tubing then slowly graduate to "medium" tubing.
I'm using the "heavy" tubing now after one month for all my shoulder exercises. By hooking that round ball (attached to small strap) inside a door,(make sure you close the door towards you), you can pull back one tube to simulate drawing the bow.
I'm at the stage where I grab both handles and pull back to "full draw" hold for 3 seconds and let down. After one month, able to draw back my 55# bow and shoot 10 arrows, twice a week. I also exercise the left arm because I shoot LH also.
You can use these bands for lower back and arm strengthening movements also. The key is start light, work up to medium. Not a bad buy at $10.