pet owner wants me to babysit dog but hasnt booked me yet?

After a M&G I immediately archive the request as owner didn't respond and give the client 48 hours to complete the booking. If they don't, I message them and ask if they still want me to keep their dog. I say that I have other requests for that time and want to give them first priority. If they respond and say they haven't made up their mind yet, I tell them I cannot hold a spot for them without payment. If they don't respond (or don't book) with 24 hours of my message, I just move on and take the next request. No payment = no reservation, much like hotels and airlines.

Communicate with your client. If you've already completed the first stay, send a message and ask if she still wants you to sit at the end of March, and if so, that you'd like to go ahead get that booked. Either of you should be able to initiate the booking request.

Welcome to Rover! I hope you're liking it so far. I've definitely been in your shoes. People's plans change so often that I never hold a spot for anyone (unless they are booked of course), and I highly recommend doing the same. You will lose money and be sooooo frustrated and resentful (like I was) with people who have no idea the lengths you're going to for them. Then they'll either not get back to you at all or they will message you right before the stay is supposed to happen and say their plans changed or they got the dates wrong. Some people don't mean to, but some people do it on purpose to avoid cancellation fees or to try and set something up off the books (never do that, by the way). Just like Emily said, send them a booking request. Include a very polite, brief message letting them know that you would love to hold the spot for them but you need it to be officially booked by Friday (or whatever day, but try to give them 24-48 hours) so you can make sure they have someone to take care of their pup.
Also, as a side note, you can mark yourself as unavailable on your calendar. Click your name at the top of your rover page, click calendar, click a date, and select "Mark as unavailable." That should prevent you from getting any requests for those dates. You can also set yourself to "away" if you won't be available for awhile.

Just communicate w the client, tell them you wanted to touchbase about the upcoming pet sitting and do initiate the booking request. Show them you have interest in them, and show them you are proactive. It works wonders :)