Our female, Aurora, who was and still is (at 16 months) wary and shy despite hours and hours of socialization, training and daycare. We eventually learned acceptance was key. Early on I would get frustrated and wished she could be more like a friendly, happy go lucky Labrador, but realized that was unfair to her. She is a guardian breed and fine tuned to detect and be suspicious of anyone or anything "strange". This also means she is going to "interview" people. She is very loving and affectionate with family, neighbors, daycare staff and trainers, but she reserves the right to let someone know she's uncomfortable if they are coming on too strong. We've learned to read when she's uncomfortable (hiding/ignoring when she was younger, backing away, stretching her front half towards the object she fears while keeping her back legs far behind, or even growling) and most importantly accepting it. I had to come around to recognizing that her being shy or wary doesn't mean she is somehow less of a dog, but that she just needs more understanding from us.
The second thing we learned was important was advocacy. It sounds like you are already doing that by not allowing everyone pet her. We've leaned to be her advocate and communicate to people to let her come to them. She will still back up from people she knows (neighbors, daycare staff) that come on too strong. So we encourage people to let her sniff them and scratch under her chin versus pat her on top of her head. Sadly when she was a younger we probably should not have pushed her to interact with strangers beyond her comfort zone. Like BoxerGirl said, socialization is not necessarily about interaction, but more introduction/exposure. We try to be more mindful now to let her decide her space and pace.
When she was a puppy we also trusted a daycare that "graduated" her too quickly to a larger dog play group. I quickly found her another daycare that was more caring and tried to accommodate her unique needs. They kept her in a puppy/small dog play group until she gained enough confidence to join the boisterous teenage play group. This daycare was also willing to incorporate specific training like dispensing treats so she could make positive associations with certain staff members. She now enjoys many more friendships (dog and human) than we alone could give her. My husband and I joke she probably has more friends than we do. It's great to see her enthusiastically run into the arms of her daycare caregivers when dropping her off and watching her play with her furry friends on the daycare videocam. In place of a daycare, you can also try to connect her with trustworthy friendly dogs. We had two neighbor adult dogs that could be completely trusted with a puppy so they met and played with our girl. She still adores them to this day although she now dwarfs them in size.
And finally training has been very helpful. As mentioned we reward with lots of high value happy treats whenever she is meeting new people, places or things. We take our time and let her set the pace of the introductions. We've also learned to try to lighten her mood with silly playful talk. For example if she's afraid of a new object we will speak to her and use a tone that belies this is nothing to be afraid of. She seems to then catch on that the object or thing is not a threat. We also took a class on training games that we try to use to help relieve her anxiety and focus her attention on something fun and rewarding.
Hopefully, reading about what we have found to work and what has not for us will help you and your girl!
