I was given three repair shops by insurance company to call for appointment. Two are out there in left field with appointments middle of March! Third one was able to go Saturday morning (Jan 21) and got estimate done and preorder parts, taking it in Jan 30th!
I just went through the same thing. My accident was 12/15 (not my fault). I was able to drive home with the bumper bungeed - otherwise it would have been dragging on the ground.
The repair shop said they couldn't look at it until the following Monday, although I was able to get a rental through my insurance the next day (Friday). But Friday afternoon I got a call from the insurance company stating they wouldn't pay for the rental I had gotten earlier in the day if my car was at my house and was drivable, so I drove it to the repair shop and left it in their parking lot. I was able to put my keys and instructions in an envelope in their drop box.
Interestingly, even though the police report stated the other driver didn't see me when she made her left turn (while I was going straight through the intersection), and the report stated I did not contribute to the accident, the claim rep conceded 10% liability because of the point of impact. So even when it clearly isn't your fault, they may charge you with some liability.
I picked up my car on January 17, so it was just over a month. Sure glad to have my 2015 Santa Fe back - much nicer than the new Mazda CX-5 I rented.