How else can I quit drinking if I don't like aa and am too shy to contribute?

Find a counselor. Some counselors can help you get comfortable with aa. With that said try smaller meetings, you don't have to talk at first. Just show up, go with friend if possible. You contribute by showing up.
Great excuse. Completely bogus, though. The only thing to dislike about aa is that they will see through every other bogus excuse you can think of (having tried every one of them a long time ago, with about the same success) . And it isn't "contributions" they expect, it's you quitting lying to yourself.