Hello, I'm Jason. I will do my best to answer your question quickly and accurately using the information you have provided.
Yes, this should be a closed system, which means that if you keep having to add coolant, you definitely have a leak.
Now, here's a compounding problem. The coolant that you used, if it's not BMW coolant from a dealer, is not compatible with your cooling system
I strongly suggest not driving the car, as if it continues to overheat, the resulting engine damage can cost you thousands of dollars
I'll hold chat open to see if you're able to respond
Unfortunately, in about 99% of cases, only the dealer will carry the proper coolant