Hi Toni ... thanks for posting the question. Before you begin to work out a safe practice for your student, you may want to inquire as to which type of hip bursitis she has. The most common form is bursitis of the trochanter (the outside of the hip), but some people get it in the ischium (the sitting bones). I am going to assume her case is the more common one, and she gets pain on the outside of her hip.
Naturally, she should ask her health care professional what she thinks about doing exercise, but normally exercises can help, but the kind of exercise is important. Walking and stair climbing can make this condition worse. Stretching can make it better.
Bursae are pads found between tendons/ligaments and bony surfaces. They help to lubricate the movement or gliding of the tendon over the bone. Sometimes they get over-stressed and become inflamed. Rarely, they may also become infected, which is why seeing a doctor is important. Normal treatment for inflammation can be helpful: RICE = rest, ice, compression and elevation. Some mobilization of the area also helps to bring nutrients into the region to assist with healing, but we don't want to overdo the stresses here.
Personally I have found that Yin Yoga poses help with bursitis in the hip. Your student might find that any pose that works the outside of the hip will help her. Try Bananasana: lying on her back, stretch both arms overhead and clasp the opposite elbows, then, without moving your hips, arch to the side. Move both your legs and your upper body. Go to where you feel a nice stretch along the side body. Also try Reclining Twist with the top leg straight out to the side, and hold that foot with the opposite hand. It doesn't matter if the leg is completely straight; she just wants to feel a stress in the outside of the hip. Hold each pose for 3~ 5 minutes.
It may take a few weeks for the condition to resolve itself. It will take longer if she keeps aggravating it (ie: if she keeps doing long walks or stair climbing or whatever created the condition in the first place.)
A good way to deal with the inflammation that accompanies bursitis is to take antioxidants. Supplements like Vitamin C, E and CoEnzyme 10 work well, but a great source of natural antioxidants can be found through earthing. You can read all about earthing in the latest Yin Yoga Insight Newsletter: http://www.yinyoga.com/Newsletter_volume4.php