I have been through this samething a couple of times in the last few years and I can tell you everything will work out just fine and not to stress yourself about it anymore.
My daughter took the birthday invitations to school and gave them out to the girls. On the invite I included my name, phone number, home address and a little note to the parents saying stating that we are having a Birthday party and my daughter would really like it if "Sara" could come by for a little while and play. I also said "please give me a call when you have a free minute so I can introduce myself properly and we can discuss the details of the party" "hope to hear from you soon".
EVERY SINGLE MOM CALLED ME! Every single child came to the party (and one mom). It worked out perfectly.
Having experienced this on the other end as well... When my daughter comes home with an invitation to a party she is soooo excited! Naturally, I will call and talk with the parents and when I drop her off I will go inside and introduce myself, leave a contact number with the parent (and with my child) just in case. I have never had a problem.
The kids will all talk about the party at school for days following the event! It is so much fun.
When you think about it, it is not any different than dropping your child off at daycare for the first time, girl scouts for the first time, or even a get together at the library. Relax and enjoy the party.. Your daughter sure will :)