The police do have the power to pull over individuals and check for licence, registration, and sobriety, but the breath test isn't random in that case because there has to be reasonable suspicion, which is another problem with this bill. Some of the reasonable suspicions and presumptions in this bill are settled case law. If there's alcohol emanating from your breath, there's reasonable suspicion. There are a lot of other cases in this bill where the reasonable suspicion standard is deluded and, in the case of the random section, eliminated.
In your case, it's not truly random if the breath test is administered because there would be a constellation of objectionably discernible facts that would lead to that decision.