When one headlight goes out does replacing the BCM fix the one headlight problem or if the BCM is bad, both headlights would be out?

Hello, the BCM controls the relays that activate the Low Beam headlamps and High Beam headlamps. So, it's divided up by the high and low beams, not side to side. If you have one headlamp out high and low beam, its most likely going to be more of a Ground for the headlamp on that side. Now if the Low beams work and high beams don't, then the relay that controls the one that's not functioning needs to be checked. Never replace a module without checking inputs, outputs, power feeds, and grounds to begin with.
These are the wiring diagrams showing how the BCM grounds the headlamp relays to turn them on:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

https://www.2carpros.com/articles/how-to-check-a-car-fuse