I consider that "take somewhere" does not necessarily imply driving or any kind of transport for that matter, but , of course, drive to school, would be perfectly correct if the transport is a car.
I haven't checked your profile, but probably you are American (??) I visited Miami once and my friend thought it outrageous that I should suggest "walking" to her university to collect her. Here in Spain, many children, not to say most, are taken to school on foot.
Bob and the policeman...sounds very good to me. I think anybody would think of a car in this context and the policeman driving.
Together they drove...could lead to misunderstandings, I think. One might understand that they both actually drove, taking turns.
Happy New Year!