I have suffered with Hip Bursitis on and off for years. There is normally a trigger which sets it off.
I have been to doctors/physios about it and had lots of different treatment. About 2 months ago I had a cortisone injection which hurt like hell but did absolutely nothing.
A couple of weeks after the injection I had a session with The Running School in London and was told it was because I 'crossed over' when running and swung my hips. Since then I have been working on strengthening my hips and running technique and touch wood my hip has been fine.
So rest to begin with ice packs and maybe have run technique looked at?