If it's your car, and if the car's still drivable, then bring it to another garage (or 2 or 3) for a quote in person.
No headlights should be ok during daylight, and I think hand turn signals are still legal in CAN/US if your signals are broken, but you might want to phone & ask at a local motoring association (AMA/CAA, etc) to make sure, a ticket for no lights/signals wouldn't make things any cheaper.
And/or you could take just the quote from the first garage, and ask other garages about how much the repair would cost if they did the work. Asking over the phone might work too.
BUT, if it were the repair bill for other car that you rear-ended you're concerned about, I think you're stuck. That owner should be able to have their car repaired wherever they want, if your insurance says it's ok & they'll be paying.
Similarly, you should be allowed to have your car repaired wherever you want. But if your insurance is paying to repair your car at a "good" garage, why do you care how much it will cost? Will your insurance rates go up less if you have it repaired at a cheaper place (maybe with cheaper or used parts, which for a bumper could theoretically be less safe)? Or are you considering having it repaired yourself & not making an insurance claim? Would that make a difference to your insurance rates, since they already know you rear-ended a car & might be increasing your rates anyway?