How do you book a stay by the hour?

I do not know of a specific option for that; however, on the computer or a mobile browser, you can go into the chat with the client whose rates you would like to customize. You will see the booking the client proposed on the left side of the screen. Click "Modify Request" and then scroll down to "Extras and Adjustments." Here, you can adjust the price to be whatever you'd like, and the client can approve these changes. So you could find out how much the total booking would cost at your desired hourly rate and adjust the price to fit and then explain this to the client (when you edit a booking, there is a spot at the very bottom to explain why you made the changes).

Please note that 20% will go to Rover in fees, just something to always keep in mind when deciding how much to charge.