Pain from shoulder bursitis can be very debilitating. You have to find a combination of stretching and exercising the shoulder, but not overdoing it to where you are flaring up the bursa.
First start off with some shoulder circles. You can roll them clockwise, and then counter clockwise. This will stretch out the shoulder and neck muscles. Start with 5-10 each way. Next is shoulder or scapular squeezes. You can use your elbows to help squeeze your shoulder blades back behind you. Imagine that someone has their hand on the middle of your spine, and you are trying to squeeze their hand with your shoulder blades. Do about 5-10 of those.
Then grab a cane or PVC pipe so you can move your arm and shoulder passively. The arm just goes along for the ride. You are moving the cane with your good arm up and down taking the other one up with it without actively moving your injured arm. This movement is shoulder flexion. Only go as high as you comfortable can. Do 5-10 of these. Next, you will do external rotation with the cane. Make sure you keep your elbow by your side when you are pushing out. You can use a towel between your body and elbow to make sure it stays close. Try not to push the whole arm out, just rotate it out with the cane.
Now you will do a scaption motion. This means your arms are not completely out in front of you, and not completely to the side. Hold them out at about a 45 degree angle. With your thumbs up, lift them up as high as you comfortably can, and then slowly come back down.
Your final exercise is strengthening with a resistive band. This will be external rotation of both arms. Again, place your elbows by your side and try to keep them there. Keep your thumbs up, and keep your wrist in a neutral position. Pull out and slowly control it back in while keeping your elbows by your side.
Those are your shoulder bursitis exercises and stretches!