I will be visiting my parents for a about 4-5 weeks over Christmas. I have a 1.5-yo cat that is very scared of most people. She is used to me and my girlfriend now, but rarely lets anyone else approach. If I can find someone to come take care of her once/twice a day she won't interact with the sitter or anyone else at all. The other option is bringing her with me, but I don't know what is the best option.
It is very hard for a cat to come to a new place and by the time your cat settles in, it is time to move back home.
So if it is possible for you to get a cat sitter, I think this is the best option for her. When you move a cat there will always be an element of stress, so in my opinion it is best to avoid this.
The fact that your cat is shy will make the travel and stay at a new place harder for her. So if it is possible for you to let her stay at home, this will be the best solution for her.