Don't be nervous! One of my first meet and greets didn't go well, because the dog didn't like my dog, hehe. Eventually, the owners said, "No thanks," to me, and went with another sitter. In spite of that, I am booked every week! And it is so much fun!
Here's what I do at meet and greets: When a client comes, I tell them I'd like to take our pups for a very short walk up and down the road just to give everyone a chance to know each other (this was great advice I followed from reading another sitter's comment in these threads). Following that, we go to our backyard where we take the pups off the leash and watch how they interact. This will tell me a lot. I never accept aggressive pups. Finally, after 5-10 minutes of socializing in the yard, we make our way inside the house, off leash. That way, the dog can get a feel for the lay of the land, the smells, etc.
More often than not, it works out. Very rarely do I decline someone. And when I have, it never hurt my business. It will work out for you, I promise! =) You're going to have fun with this! =)