@Christine546, I am not a lawyer, but I am an AirBnB host in San Francisco.
To get to the quick answer, most AirBnB hosts just register as Sole Proprietorships.
Longer answer (still not a lawyer, but I have started multiple companies):
There are lots of choices about what entity to use to start a business (anywhere, not just SF).
The critical difference between a Sole Proprietorship (and the related General Partnership) is that a Sole Proprietorship / General Partnership is not a separately taxable entity. That means a number of things, but for AirBnB hosts one big thing is that you don't have to pay the $800/year California minimum franchise tax.
One thing you do NOT get with a Sole Proprietorship / General Partnership is limited liability protection, but there is a strong argument that the limited liability would be of little usefulness in the AirBnB situation.
(The property isn't owned by the entity, and you are probably personally doing all the work anyway.)
So unless you have a strong personal reason to use one of the other entity types, most people choose Sole Proprietorship for getting their Business License for AirBnB use in San Francisco.