Hi, Kristina. There isn't a way to have the quoted price automatically reflect that. You can, however, manually change the price to reflect this after you and the client have discussed pick-up and drop-off times. This will let you manually put in whatever pro-rated cost you want to the client's booking.
For the website:
Once you have received a request and clarified your policies, as well as the preferred pick-up and drop-off times, you can let the client know how much you will add to their booking. Then, you can push "edit" next to the listed "Stay Price". The website will then pull-up a box where you can add a "Cost Adjustment" of a one-time price inflation.
For the app:
Once you have received a request and clarified your policies, as well as the preferred pick-up and drop-off times, you can let the client know how much you will add to their booking. You can push "Modify" at the top of the conversation where you will see a new screen. Click on "Cost Adjustments" and add the additional cost onto the booking.
Note: Just make sure that you clearly outline your 24 hour policy on your profile, as it will be different from other sitters on Rover.