I'm not gonna bring my new girlfriend to the wedding I was invited to.
Why don't you want to bring your girlfriend?
It will make an awkward atmosphere at the wedding.
It's normal not to bring a new partner to important events such as a wedding. There's nothing wrong with waiting until you are more comfortable with your girlfriend before bringing her to events like that.
I hope she will understand.
I'm sure she will be fine with it. If she does get upset about it, just explain to her how you feel. If you calmly discuss your feelings, I'm sure the two of you can work through it if it does become an issue.