Say you're a young worker at a multinational company going out on a business meeting with your boss in her car. Considering that she is quite senior and a female too, where do you seat? The passenger side, or beside her at the back?

Why not ask her? If you are not the driver, sit in the back with her.

Depends on how senior the boss is and the level of familiarity. It is safer to err on the side of caution. Sit in the front. If your boss thinks other-wise, s/he can ask you to sit in the back.
It's akin to taking a seat in an unfamiliar senior's office before being asked to do so.

My boss considers the issue mundane He just goes to the front with the driver. Na u sabi wetin you wan do for back.

Fortunately for me, my boss drives himself so i sit with him in the front.

We normally use pool car when we go out together and we both sit at the back. In few times we go out with her car, I normally prefer to sit in front, while she sits at the back and her driver drives. But in rare cases, I sit beside her.