When you begin a stretching routine while you have an injury or a condition like bursitis, the key is to do it VERY gradually and gently.

Here is how I like to describe the process...
Put you hand flat on the table, fingers and thumbs stretched out "as far as you can." Now, concentrate on stretching your thumb and little finger a little bit more - it may only be 1/4" - and hold for 10 seconds. Relax & repeat 3-5 times. You may get it them to move a little more, or not.

Same with the hip - The "stride" is a good example. Bend the front leg 50-60 degrees, more if you can. Make sure you can see your toes in front of your knee. Then keeping your back straight and head up (you may rest on hand on a table for balance) SLOWLY and GENTLY push your butt down until you feel a pull in the front of the thigh on the back leg. Hold 15-30 seconds. Relax & repeat 3-5 times, then do the other side.
The legs crossed or "hip thrust" is another good gentle on to start with - again push out slowly to the point of firm resistance, hold and relax.

When my bursitis flares, I try to do these after a warm shower, and maybe rub on some topical Voltaren. (If you can take ibuprofen, you can try that 1/2 hour before stretching too.)

Have you thought about requesting a consult with a PT to get the exercises right?
Sue