Liking someone is often just a matter of a moment. Maybe your tempers and personalities are totally incompatible, but love is there, so what? She is a quiet girl, and a rash confession will scare her. Let me give you a few suggestions:
First, slowly get closer to her, starting with being friends. Such girls will get used to this way of approaching, and the natural deepening of feelings will make her feel at ease and warm.
Second, you can give her a small gift first to test her feelings. A simple and creative gift will do, such as a crystal music box. I think a quiet girl will like the pure crystal and beautiful melody, and I believe she will also know the meaning. Of course, you can also give her a small teddy bear, which is very cute and she will definitely like it.
Third, ask your friends to inquire about her, and also learn to inquire from the side, which will make her pay a little attention to you, and it will be easier to approach her.