Hey Professor, consider yourself very lucky re avoiding gunshyness in a pup showing up at a gun club. Many people only introduce the gun while a pup is chasing game and then they hopefully don't even hear or don't care due to the game interest when ONE single gunshot goes off. Some pups are way more prone to gunshyness than your dog. It appears you lucked out because usually an ounce of prevention is worth more than a pound of cure when it comes to bird dogs and avoiding gunshyness.
I always figured any dog is going to be gun shy. My last two dogs were both gun shy at first. This last one, my present one, a Springer Spaniel was scared to death. I just took her out to my club on a day when they were having a trap tournament held her on a leash behind the pads, walked her around and let her get used to it. She was terrified of the noise. But she got over it after a couple times out. She was loving the attention she got from everyone, she soon forgot about the noise. Now it doesn't bother her at all. Next time I'll probably try Brent,D's method. Spend a few hours with her in the car, first. Then ease them out. Take care.