There are several tips of hip bursitis as it always goes back to anatomy. Trochanteric bursitis which is lateral to the hip. Which creates pain along the lateral hip.
Then there is iliopectineal bursitis where the bursa is located mid femur and the pain is located more in the front that can refer up into the hip.
Depending on which type the person has, you want to avoid deep hip flexion or squats that will
irritate both types.
Training should focus on strengthening the glute medius, glute max as well as strengthening the core.
It is also very important to stretch the hip flexors, quadriceps, ITB and quadratus lumborum.
I assume your question is about exercises for people who suffer from bursitis in the region of the greater trochanter. I also assume that the person has seen a doctor and is receiving appropriate treatment to reduce the inflammation and is cleared to exercise
The best you can do for this client is to do an assessment and see whether some imbalances may have contributed to the client getting bursitis in the first place. You can address those with appropriate exercises. Else, make sure to strengthen the leg and hip muscles to prevent a recurrence of the problem.