Client not responding?

It sounds like she may have booked someone else and she may not let you know that until much later, if ever. It happens. Sometimes, the person indicates that they want to book you and it doesn't happen. If this person found you through Rover and both of you didn't confirm the booking on Rover (it would show as booked in your inbox), then No Booking exists. You're free to go ahead with your day. This wouldn't cause you any problems later. A client who hasn't booked cannot leave a review (based on a service that wasn't booked/didn't happen).

For the future, if you want the booking, communicate earlier to make sure it's confirmed as soon as possible after the meet&greet,

Was the booking actually confirmed? You can tell because not only did one of you have to click the Book Now button, the other had to confirm/accept. At that point the request would have moved from the Pending tab to the Upcoming tab. If the booking had not been finalized then the client likely found another sitter. If it was fully booked and she hasn't responded, I would send a message letting her know you'll be gone between x hours and please message you back to schedule a new drop off time.

Here are some tips I've learned that may help. During the Meet & Greet I ask if they know the drop off and pick up times. If they do, great, I note it down. If they don't, I just ask them to let me know when they find out. If we discussed booking, I generally tell them I'll accept the booking and they must confirm to finalize (especially new clients). In cases where it's months or weeks in advance I let them know Rover will charge their credit card upon finalizing the booking and offer to let them wait if it's an issue (they stay in my "pending"). If I submit the booking by clicking "Book Now" and the client does not accept within the 72 hour period, I reach out to them. If they don't respond I assume they're booking with someone else. A few days before the booking, I reach out to confirm the booking and the drop off and pick up times (more of a reminder), and ask them to let me know if anything has changed.

I hope this helps! Good Luck!

Stuff happens, it is possible the client changed their plans. Do you have a confirmed booking? If the client reaches out to later you'll just have to reschedule the drop-off to a time when you are available.