I keep thinking about the timeline, okay....she left for work, minutes later she texts she forgot her badge, her carpool states she will wait the ten minutes. (then nothing right?)
If her badge is truly at home still, I assume whatever happened, happened minutes later either where she stopped to turn back home to get her badge, or at the home. I do not think she went to the bus terminal to take a bus. If your friends with your carpooling coworker, your not going to leave them sit waiting on you. Your going to text them or call them and say...."Go ahead, don't be late over me, I am catching the bus, or cab or husband will drop me off" etc. Your not going to leave that gap, that is just rude actually, and I just don't see it from a professional woman. IMHO