If your mother's car is a BMW then the costs are going to exceed $500. I've seen too many shady repair jobs to want to have it repaired. If she's not at fault she shouldn't have to pay for any of the repair/replacement costs. I personally have all my work done at the dealership and I've found that bumper replacements are quite costly. Here in Korea the replacement + labor runs near USD 10K. If the sensors got damaged, then it's going to cost more.
I hope your mothers okay. Hope the other drivers are as well.