When you walk with this kind of limp, the front hip flexors that twist the thigh in are tugging the iliotibial band forward, and straining the gluts.
The exercises you can perform to reduce the risk of hip bursitis is to stretch your tensor fascia latae, and strengthening your hip external rotators, hip abductors and hip extensors.
To stretch your tensor fascia latae, lay on your good side, pull your top foot to the buttocks, keeping the foot close to the floor; then put your good lower leg on top of the painful thigh and stretch. To strengthen your hip abductors, lay on your stomach and slide your leg out like a snow angel. Stop at 30. To strengthen your hip extensors lay on your stomach with a pillow under your waist. Bend up the lower leg and lift the thigh to the ceiling. Stop at 30.