Definitely what Walt said! But I'm curious because I'm not totally clear on what you meant by the first couple of sentences. I think maybe if I'm interpreting it correctly you are maybe thinking you can't accept requests without a Meet & Greet? Or you don't know where or how to schedule Meet & Greets? If either of those is the case, here's a bit of information for you.
In person Meet & Greets are not required; you can book without them. Meet & Greets are highly recommended (not just by Rover but by those of us who didn't do one and ended up with a bad experience that a Meet & Greet likely would have either prevented or make us realize the dog was not a good fit). I think you're concerned b/c of COVID-19? If so, at the end of the day this is an "essential worker" job and if you choose to do it right now, you are taking a risk. However there are ways to minimize the risk. Go ahead and have the Meet & Greet but wear a mask and ask the client to do the same, stay 6 feet apart, don't touch the dog's leash or collar/harness (feel free to pet the dog though!). Wash your hands thoroughly right before and right after the Meet & Greet. Alternatively, you can forego in person and do a "virtual" meet & greet through messages, video, or voice call.
Another thing I've found is that the initial reply usually gets more response when it's kept short and more of an acknowledgment - I usually say something like "your dog sounds adorable and I'd love to care for him/her". I do boarding and doggy day care so I always ask, even on that first contact, how their dog is with other dogs (or if it says they're good with other dogs I say something like, "it looks like [name] is good with other dogs; I usually have 2-5 here of different sizes. If it's for a walk or drop in I generally still start with an expression of interest. Then I say I'd love to meet so the dog can get to know me first and I can understand any needs or preferences, but I do understand that with quarantine you may not be comfortable meeting first so we can chat through message/voice/video - whatever their preference. Even though we are in quarantine some clients still want to meet and honestly, I prefer not to take a dog I haven't met before. As to where you'd meet - it's where ever the care is going to happen. If it's in your home, they'd come to you. If it's their home, you'd go there. Just try not to touch anything. Remember wash hands, wear masks, and stay 6 feet apart from the other people.
Good luck!