How do you charge for several hour dog sitting?

There is no way to charge on an hourly basis in Rover's system. You'll have figure out how much you want to charge them, then book it as a one night of house sitting, making an adjustment to your nightly rate. Use the Modification feature on the billing invoice. Alternatively, you could book it as a drop-in and then modify upward, but then you'd have to start a Rover card, etc. Using house sitting would be easier.

House sitting with a discount that you enter manually. I personally, when I used to house sit, would charge a regular rate even if they needed less hours. No one ever suggested they wanted a discount. But of course you can give them a 50% discount if you feel that's the right thing to do, and you enter it manually.