To get a perfect score is a difference of 12, birds hitting you needs to be the lower, obviously. Ex.
Balloons: 14
Birds: 2
This guy, BizKit does many videos relating to Square games and he did a vid getting a perfect score on the Chocobo Race.
http://www.youtube.com/watch?v=6vncNMQrFv8
He handled it better than me, my score was 15 balloons and 3 birds.