The invoice should have had a breakdown of parts and labor costs. Most auto repair places that I have used in the past charge an hourly rate for labor and use a manual that determines the standard labor required for a repair. If the repair is supposed to take an hour, for example, then the labor charge should be whatever the shop bills for an hour. Many states also require the shop to return the broken part if requested, so presumably the customer could verify that the part was actually replaced. There can be a tremendous difference in price from one after market part to another, and most repair shops will tell you that they will not guarantee parts that are not provided by their part supplier.
You should be able to find the labor schedule and a range of prices for the part on-line relatively easily, especially for a popular make like BMW.