How often (frequency) can my wife receive celestone/lidocaine/marcaine injection for her sciatica (lumbar foraminal narrowing) and hip bursitis?

Safety. Safe is as few injections as you need to get relief. However if you need these injections regularly, safe is a relative term but typically around 3-4 injections/year. Some patients can have as many as 3 injections per 6 months however that is not a good idea for too long.
Depends! I usually will ject the trochanteric bursa up to three times without concern. It is not weight bearing and the meds do not enter the hip. Generally most physicans who perform the block will stop after "a course of three." I do not believe this concept. If no relief is forthcoming after the first, it becomes increasingly unlikely that a 2nd or 3rd will help. A sciatic nerve block can help.
Further evaluation. I agree with the responses already provided which is 3-4 injections per year. If symptoms persist further evaluation may be helpful. Often chronic hip joint bursitis is due to underlying tendinosis of the gluteus medius/maximus muscle. Persistent spine (foraminal stenosis) problem may require a surgical evaluation. PT should certainly precede these invasion steps.
3 per 6 months. One needs to be careful of excess steroid exposure. 3 injections in a 6 month period is generally seen as safe.
3 times. It's generally accepted that people shouldn't get more than 3 shots in a year. Steroid injections can weaken the surrounding tissue, which is why there is a limit.