AITA for staying at the museum after my friend said she'd had enough?

At two o'clock, my friend Beth said she wanted to go home. I was halfway through the gallery I'd most wanted to see.

We had driven there in my car. Before leaving, we'd agreed to head back at four. Beth doesn't drive. She'd said the exhibition sounded interesting, though she'd never been to this museum.

After an hour, she was bored. I was stopping to read the descriptions while she waited by the exits. When she asked to leave at two, I reminded her about four. She said she hadn't realized two more hours would feel that long.

I said, "You're free to sit in the gift shop if you're done." She went quiet, then booked a taxi home for $34. I offered her the car keys so she could wait in the car, but by then she'd ordered it. I stayed until four and drove back alone.

Beth now wants me to pay half the taxi fare because I was the person who wanted to stay. I don't think changing the departure time should automatically have become my expense. But my gift-shop comment treated her like an inconvenience rather than someone I'd invited for a day together.

We had agreed on a time. We hadn't agreed that one of us might spend half the afternoon waiting for the other. AITA for staying?