I want to go to a music festival without my girlfriend
Why wouldn't you want to take your girlfriend.
I know my girlfriend doesn't like this kind of music, but I really want to go there.
If she doesn't like that kind of music then it is fine, it is okay to want to get away from your girlfriend every once in a while. You would get tired of her if you never got time away.
But what would I expect her to do while I'm busy?
Your girlfriend can do whatever she wants while you are away.  Just make sure that she is okay with you going away without her, and if possible, allow her to take her own time away whenever she wants in the future.