Can’t get an estimate at my mechanic if I’m not sure I’m fixing it at all…
Geico said they won’t send someone down and I have to bring it to their mechanic to get an estimate and check.
I would absolutely take it to a mechanic BEFORE Geico looks at your car. In fact, I would take it to at least two, if not three, mechanics. You won't know if you are fixing your car until you know how much damage was done. Are you an expert in figuring out how may screws, bolts and unseen mechanical parts are necessary to fix your car? Any mechanic who gives you an estimate has the potential of being chosen to fix the car. You won't know until you get the estimate.
To be yasher, you can tell the mechanics that you want to get an estimate to possibly fix your car. (I probably would not tell them I am getting more than one estimate.) You may be surprised. You may find yourself a mechanic who really knows his stuff more than your own. You are assuming that the insurance company who is at fault may try to minimize the damage that is done. They may go for straightening a metal piece (leaving pock marks) instead of buying a new one or just doing a touch-up paint job (with mismatched coloring) instead of painting the entire piece.
This way, you are armed for the Geico estimator (the adjuster decides how much you will get based on the estimator's estimate) to make sure he includes everything. Yes, you can negotiate with the estimator and adjuster by treating them with respect and care. This is best done in person at the time when you give them a cold drink on a hot day, etc. I would call Geico's claim department and ask what their policy is regarding them getting an estimate (before giving them your specific info, because then it will certainly go to the same adjuster).
When Geico (or whichever company is at fault) is ready to pay, you may request that the check go directly to you instead of the car mechanic. This is what I have done in the past, but I believe it may be your right even though they may tell you it must go to the shop. The amount you negotiate with the mechanic who eventually will fix the car (or not) has nothing to do with the exact amount of the check that you receive.
The other guy's insurance might go up no matter how much the company pays out and I believe it might even go up at any "at fault" incident that was reported, even if nothing was paid out (need to double check that). This is the reason you and he pay insurance premiums.
ETA I wrote this as a general procedure, not necessarily for a minor scratch on a fender. It is up to you if you want to accept the slight damage on your bumper as a potch from Hashem without going through the hassle yourself and expense for the other guy.