This is a hit and run accident. The lady and her insurance company will need to eventually pay for all damage to your vehicle (bike.) The law says that anyone who hits another vehicle from the rear is responsible. You might have a problem since this ocured at night. Were you and your vehicle properly lighted and reasonably visible?
You have vehicle damage, and I would assume some physical damage to you requiring some medical attention. If not immediately, then a few days later with aches and pain. Go see a doctor right away.
Don't talk with the lady's insurance company, telling them anything other than you were hit from behind by their client. There is a police report. You'll be glad to talk with them in the future when you file a claim. Youn have meybe two years from now to file a claim.
Her insurance policy probably has a few thousand dollars in it to cover immediate damages. Ask them to replace your bicycle now so that when you recover from physical injuries sometime in the future you will have transportation. If you have serious physical injuries to yourself, how are you able to ride a bike? Your doctor should give you an estimate of when you can return to different activities. Returning to certain activities does not mean the same as full recovery from your injuries.
Unless they can prove you were negligent or at fault, they're screwed. Maybe get a lawyer.