So this is why stores offer free mattress delivery. If not, they are pretty much liable for public hazards like bringing a mattress on the bus. I totally don't blame this woman though. My uncle had a similar situation when he lived in New York. He bought an entertainment center and had to take it piece by piece on the bus. It took him a year and a half. That's why I'm all about driving a lifted four-wheel truck.
You can't deny this woman her right to ride on the bus, but that's also the most inconvenient thing in the world. People on the bus are just trying to go home or go to work. There's a zero percent chance they're going to have any time for this. Even worse if someone decided to have an accident on your brand new mattress.