i've seen quite a few patients with Trochanteric (hip) bursitis, and they usually go for the cortisone injections with good effect (only when symptoms persisit though) maybe you should speak to you doctor about it, find out more about it so you can make an informed decision. if you definately dont want to take this route, then there are a few things you could try.
the first thing is restrict your movement and allow the joint to heal. it is important to rest the affected joint.
apply an ice pack, which will help to control the inflammation and reduce swelling. this will help the bursa to return to its usual state and function.
and since bursitis is inflammation of the bursa, continue to take anti-infammatories, which will help with the pain.
there are other home remedies, which you can find by surfing the net, but you must use caution and involve your doctor to ensure your safety. heres a link for you to look at.
http://www.anysubject.com/bursitis-bursitis-sy mptoms-bursitis-treatment-diagnosis-coping-wit h-bursitis.asp
hope this helps, take care and best wishes xxx