You have a two options with insurance.
1. Go through your insurance. You will have to pay your deductible up front. They will handle the repairs to your car and then go after the other parties insurance. When they get the money from the other insurance they will refund you your deductible. (sounds like where you are going right now)
2. Work directly with their insurance. They will handle all claim and your insurance will not be involved.
Regardless of which way you go the process is as follows:
The insurance company will send out their adjuster. The adjuster will inspect your car, take photos, and write up an estimate. They will go over the estimate with you at which point you will have a couple options. Most insurance companies have "preferred" shops that they work directly with. If you go with one of those you will just need to take your car there and inform them of the claim number and company. If you want to take the car to your own shop the insurance company will cut you a check (either on the spot or mail it to you).
I would strongly urge you to take the car to your own shop. Preferably one that is BMW certified (contact your local dealer to find one). It is your right to have your car repaired at the shop of your choice. If the shops estimate comes in higher than the adjusters (very likely), the shop will work directly with the insurance company to resolve the difference. You WILL NOT HAVE TO PAY.
Also, the insurance should provide you a rental car for while your car is in the shop. You may have a harder time with this going through your insurance though. Also, don't expect another BMW for your rental. They only need to compensate you for the loss of use. A Toyota Camery is just as useful as a BMW.
Bottom line is, you have the right to have your car repaired to the condition it was in before your loss. You also have the right to be provided a suitable replacement while yours is being fixed.