There are many things you can do at this party. A great way to get started is to get a pack of folders and fill them with some information about yourself. For example, if you have some "letter of recommendations" that will show the parents that you have experience. With permission, you could also have the contact info of the person that wrote it. You can also write a short letter stating why you are different than other babysitters, for example specific activities you do with children. On this letter also state any certifications and classes you may have participated in.
Due to my time restraint, I can list one more thing. When introducing yourself to the parents, don't try to sell them. Spark up a conversation with them, compliment their children or ask them how they are enjoying the party, then after they have felt comfortable with you and you have made them smile, then you end with, " we'll if you ever need childcare, I am available, I love children, I love teaching them new things and I would love to care for your child when you need it. Hand them the packet, smile and move. On to the next one.
If you want to get parents to come to you, do free face painting. This costs less than $10.00, but it will get you a ton of traffic and a lot of opportunities to talk to parents and show your connection with children.
The book: How anyone can make big money babysitting and have a lot of fun doing it.