There aren’t too many studies just on the duration of pain relief with steroid injections into the joints. Results range from one week as in your case up to 13 weeks.
It’s clear that steroid injections work better than placebo injections with saline solution. And studies show that some steroids work better than others. Long-term pain relief may require a higher dose of the steroid.
In some cases steroid injections are used to control pain and reduce rehab time after arthroscopic surgery. In a patient with recurring bursitis there may be other factors such as posture and overuse to be addressed. The injection may help calm the joint enough to work on improving alignment and motion. Combining physical therapy with steroid injection may be one way to improve overall results.