If she is your bestie, I think she owes it to you to tell you what she thinks is “wrong” instead of making it a guessing game for you. It may be that she is only comfortable with people she already knows or that there is something about meeting “family” that is overwhelming to her. If so, this is a problem to solve, not a reason to avoid the issue.
If she continues to be unwilling to meet other people who are important to you, I do think you should step back from “best friend” status. Her demand or inability to tolerate sharing you with others you care about will make it difficult for you to maintain your other relationships. You may find yourself having to choose between spending time with her or your family and other friends.
Please don’t limit yourself to one good friend. It is best for your self esteem and your mental health to have at least a few good, good friends as well as family in your life to share both good news and difficult times.
I wish you well.