Perhaps instead of considering a dedicated week at camp or in a "program," you could create a daily program at home. Confidence comes from accomplishment. Accomplishment can be doing very small things that were previously scary or challenging.
For example, I was intensely shy as a teenager (and still am). Talking to people scared me to death (still does) but I forced myself to face my fears. First I practiced looking people in the eye when we communicated...well, they would talk and I would look at their eyes and not their shoes. I started with the kind ladies at my local library, worked my way up to the bagging clerk at the grocery store, to the cashier, to my teachers, anyone. Once I could do that, I moved forward to smiling a hello at them. Next, I would say one nice thing to each person. Then I had to say it loud enough to be heard. After YEARS of slow, steady work, I campaigned to do a homestay abroad program. Yep, quiet shy S. spent 4 weeks in Glasgow, Scotland, UK, living with a new family and learning how to get around. After that, while I was still naturally shy, I knew I could get along in the world. People still scare the bejeebies out of me, but as a high school teacher of 20 years, people are my life. I've learned to face my fear of people and win. And, yes. I'm a very confident person.
And this is what I did ALL BY MYSELF AS A TEENAGER! Imagine what your daughter could accomplish with your love, support and guidance. Start small. When you go out, she must look up and greet at least one person, not you or a family member. It could the cashier, the person who assists you at a store, the waitperson at a restaurant, you name it. She doesn't have to say much. A simple, hello, goodbye or thank you will suffice. Once she sees that a) she can do it, b) people will like the interaction, then, hopefully c) she'll start to gain confidence. Make sure you go out at least once a day so she can practice.
Another idea is to enroll her in a class that is a group class but still very individual. For example, a tumbling or gymnastics class. My eldest son took a tumbling class that had 7-10 kids in it. But, everything they did was generally solitary, like walking the balance beam, doing a set of tumbles, etc. This way, she'll BE with people, but won't necessarily have to interact with them outside of a greeting, a good bye or a friendly cheering someone on. Me...I took dance classes. I was a terrible dancer and I didn't much like talking with the other girls, but I learned how to project a persona on stage.
Last but not least, enlist the aid of her teacher. Many shy kids blossom if they have a classroom responsiblity that they must fulfill every day. Perhaps she could take attendance to the office, water the classroom plants, hand out the color crayons, anything. For example, if your daughter was in my class and you asked me to help her with her shyness, I would have her collect all the work to be handed in, row by row. Then, I'd have her say thank you to the head of each row. Then, she'd have to look at the person in lead seat and say thank you, and so on. The list of things she could do to help me is fairly long.
Whatever you do, I would caution you to not make shyness a bad characteristic to have. I may be shy, but when I make a friend, it's generally a long term deal. I may not have a lot of friends because I'm shy, but the one's I have, I KNOW I can count on them, no matter what. I would say that's a positive. My husband and eldest son are VERY outgoing, everyone is their best friend, and they tend to get snookered a lot by the less than honorable people of the world. It's a tough lesson.
There's tons more I could say on this point, but this is too long already. Anxiety runs in my family. My mom has let it rule her life for 50 years. My sister was in therapy for years to get past it. I was the only one to strike out on my own and be so successful at it, no one ever knew how shy and scared I really was. If you'd like more ideas or to discuss further, feel free to private message me.
Good luck.