Advice:
Firstly there is no question of fault. He has a claim against you, even little impacts can cause big scratches depending on shape of your number plate etc.
The problematic question is the amount. The sum is disputed and since there are really inferior, really expensive and really corrupt repair places, a survey or even showing the receipt will not do. Unless you go to the authorized agent which will not be corrupt but will be expensive. For one thing, you have to pay for the matching metallic paint that BMW uses (about $250), plus either a new bumper or his repairs.
You should do a survey and make a fair offer. If the sum is disputed, you will have to go for mediation or respond to his legal action.
It may be tempting to get your insurer to pay the $1500, and just pay the excess of say $900. This is not a good idea since no claims discounts will be lost for amny years and the loss will definitely be in the thousands.
There is no such thing as a slight bump. The car weigh nearly 2 tonne, and that weight moving has a lot of force. Yes the bumper can absorb the force, and visibily the damage is very slight. but beside the bumper the holders would also be out of alignment.
You may say it is only a slight bump, but when he takes the car to the showroom workshop, they will check the chassis for any distortion regardless. The chassis is part of the safety feature that should compress and absorb force in a collision, therefore a slight collision could have the chassis shorten by 5mm. This would require pulling it back to the manufacturers specification. German cars are precision made, so any slight distortion would affect other moving parts.
The BMW still can run, but in time to come there will be noises here, squeeks here and there as the parts rub against each other and wear out faster.
Without all that, the bumper, paintwork and workmanship still cost a bundle.
As driving instructors like to tell their students, Don't hit a BMW or a Merce.
You may want to take into consideration for the BMW loss of usage. While his car is in the workshop repairing, he may rent another BMW which will cost a lot.