Yes, this CAN be normal for some pit bulls. A confident pit bull will usually NOT bark or put up aggressive displays before attacking - they just go for it.
And yes, there are things you can do that will improve the behavior of all but the most aggressive dogs.
One question - when you say you were "trying to keep Petunia calm" - how were you doing that?
Obedience training is the key. A dog can't attack another dog if it's in a Sit or a Stay.
For example, my dog wants to go towards other dogs she sees going past us on our walks. She has been obedience trained, so I simply put her in a "heel" BEFORE we get close to the other dog. If she tries to lunge, I correct her for BREAKING THE COMMAND, and NOT for showing aggression. This way she does not associate the correction with the other dog. If she heels nicely past the other dog, she gets major praise and occasionally a treat.
You cannot stop your dog from feeling aggression towards other dogs, but you CAN stop her from acting on it. Keep going to obedience school, and practice obedience with her everywhere so she doesn't think she only has to obey at school.
If you dog acts up, immediately begin an obedience drill (once she really understands the commands) wherever you happen to be. She must learn that obedience is not optional.