I've had bursitis in the hip and in the shoulder.
With the hip I tried lots of different treatment, physio, medication. One of the last resort after 6 months was the cortisone injection. Its took two days and then it was gone, it was amazing and I wondered why I took so long to have the injection.
Late last year I had bursitis of the shoulder. My immediate thought was cortisone injection. I had to wait 10 days until I could get it done, a backlog in treatments. The doctor ended up injected my shoulder 5 times all at once, painful.
However it was very different with the result. Very little relief even after 3 weeks and more. My physio said that hip cortisone injections were much more successful than shoulders, as the shoulder had more bursers.